Well.
If it is a quilt that was made to survive the test of time and be an heirloom, this little "incident" with the cat being all scratchy on it shouldn't have permanently damaged it. Broken it in early, yes. But...quilts last for 20-30-40 years, right? I know you've put a lot of hard work into it. I'm hoping you used your very best fabrics to take a bit of a beating. :D
Go ahead and wash it. Front loader sounds great, less likely to get all twisted up like a top loader. Maybe even spend a day at the laundrymat to use one of their jumbo ones.
THEN...after you do all the quilt show stuff...perhaps you can make a quick coordinating sashing for where the cat does it's clawing? Like, do not spend a ton of time on it...muslin back, coodinating color front, birth that sucker and put some pretty edging on it. Why? Well....here's why:
Return their quilt to them and thank them for letting you borrow it for the show. Let them know that you washed it on GENTLE and TUMBLE DRIED it so you could spiff it up for the show, but so's not to **do any damage** (see where I'm going?). Then tell them you whipped up the drape (I don't really know what this is called...all the fancy schmantzy hotels use them) because you noticed the kitty had done a little scratching. Then say something about it would be MUCH easier to replace (the drape) than the entire quilt...since some of it is HAND DONE and took many hours.
Somehow work in how much you loved working on the quilt, and you're so glad that they use it every day. And how you want them to be able to use it for a long, long time. (Because you do!)