There are a number of versions of the story of the founding of the Order of the Garter, most of which seemed based on Froissart's account. Some of the versions seem to provide an incredible amount of detail and dialog; clearly many authors felt the need to make the story as good as possible. Costain provides a short, modern, version along lines that seem to be generally accepted:

"The daughter of a handsome Burgundian knight and Sibyl, the heiress of Tregose, Katherine de Grandison had inherited wealth from her mother and beauty from her father. When David of Scotland laid siege to Wark Castle, the seat of the family, it happened that her husband ( William de Montacute, 1301-1344, ed.) was a prisoner in France and so the conduct of the defense had fallen on her slender shoulders. The fair Katherine showed a rare fighting spirit and held the invaders at bay with a small garrison consisting of the constable, a few knights, and not more than twoscore archers and servants.

However, the wail of the pipes around the walls day and night had begun to weigh on her, together with the frequent sound in the distance of Hey, Tuttie Tatie which meant that more of the wild Scots were arriving. When she saw an English army approaching with the royal standard carried in the lead, she was delighted beyond measure. It is quite understandable that she lost no time in discarding the chain-mail jacket and the steel helmet in which she had subsisted for so long and arraying herself in her very best raiment to welcome the king.

The fashion in clothes for ladies of rank had been changing, at the dictate of France. No longer were they content to appear in the loose flowing robes which afforded such slim chances of displaying their charms. When she went down to the drawbridge to greet the king, the fair Katherine wore a tight inner jacket of a tawny shade, buttoned straight down in front, and over this a very gay surcoat of lustrous brown and gold, with the hanging sleeves which were the very latest thing in feminine attire, and a very fetching device indeed. The surcoat was elaborately embroidered with the heraldic quarterings of the family and with a great many garters in a variety of shades. To borrow a modern word, there had been a "run" on the garter as a symbol for decoration. It was used for the men quite as much as for the ladies, and the royal accounts refer to a blue taffeta bedcover "powdered" with garters for the king himself. Another item is found of a jupon "for the king's body", with garters and buckles and pendants of silver gilt.

The king had a roving eye and a plausible tongue, but he was silent as he followed the chatelaine to the best chamber in the castle. Wark was one of the very earliest Norman castles and so was little more than an empty shell, the great hall extending clear to the beamed roof and the personal apartments being mere cubicles along the outer walls. The king was to have the lady's own chamber, which was little larger than any of the others but warmly furnished, no doubt, with rugs and hangings. It was reached by a steep and dark staircase opening off from the entrance.

The story runs that when they reached the entrance to the tiny room the king seemed disposed to take advantage of her husband's absence. Much to his surprise, he was rebuffed, gently but firmly.

She returned sometime later to summon him to the evening meal, which was spread out on the long table in full view below, and was somewhat disconcerted to find that he had not arrayed himself in his full finery but apparently had spent the interval in thought. He paused in the doorway and regarded her with somber eyes. She began to regret then that she had gone to such pains with her own attire, fearing that he had misconstrued her motives.

"I pray you will think well of what I have said", stated the king, "and so have the kindness to give me a different answer."

"I hoped, gracious liege," she replied "that the good Lord in heaven would drive from your noble heart such villainous designs." The she paused before going on. "I am, and ever shall be, ready to serve you, but only in what is consistent with my honour, and with yours."

The king was silent all through the meal and he left at an early hour the next morning. He had quite apparently given the situation much earnest thought and had arrived at a decision in line with the principles of the new order. The first thing he did on reaching his camp was to give instructions that the Earl of Salisbury, her husband, was to be ransomed and brought home at once.

This was how things stood between the king and the virtuous lady of Salisbury, if the story is to be believed, when a great ball was held a Windsor Castle to inaugurate the order. The earl had been brought back in the meantime and Edward, according to Froissart, "expressly ordered the Earl of Salisbury to bring the lady, his wife... All the ladies and damsels who assisted at this first convocation of the Order of the Garter came superbly dressed, excepting the Countess of Salisbury, who attended the festival dressed as plainly as possible." ...

It happened that the good lady had the misfortune to lose a garter during the dancing. This was quite a common occurrence, for elastic materials were still a matter of the distant future. Although she was plainly attired on the surface, the fair Katherine had seen to it that the accessories she wore were of the best. The garter was a handsome little trifle, of fine silk and most neatly jeweled. Knowing to whom it belonged and being "in full knowledge of their lords feeling," everyone smiled when he paused to survey it as it lay on the floor at this feet. Observing this, he stooped and picked it up and then fitted it on his own sleeve, "Honi soit qui mal y pense [Evil to him who evil thinks]", said the king in the hearing of all.

Other writers accepted the incident but disagreed as to the identity of the lady. Some said it was Queen Philippa ... Still others contended that the lady of the story was none other than the Fair Maid of Kent , who later married the Black Prince. ... The Fair Maid, a great beauty but a far from amiable lady, ... would most certainly be at the ball and, from what is known of her character, she might even have been capable of loosening her garter to attract the king's attention. Edward may not have been in love with the wife of his old friend (the fact that Froissart tells that story in such detail inclines one to believe there was some degree of truth in it), but there does not seem to be any doubt at all that the king entertained a secret liking for his beautiful madcap niece; secret only in the sense that it was never openly avowed even though it was the cause of much sly gossip about the court." (Costain, pp.312-315)

Sources:
The Three Edwards: A History of the Plantagenets, Thomas B. Costain.

http://www.montaguemillennium.com/familyresearch/garter.htm