Hi, TruthSeeker. Welcome to the Grumble!
If this is a Mother's Day gift, and you have no way to get a new mat, you could try covering the flaw. Maybe you could buy some flat lace trim, then attach it to the mat, all around the outside. If it's wide enough, it would just cover that spot. Kind of a crazy idea, but it would hide it, and she might like it. If you do, it might be a good idea to remove the damaged surface, as like Jim said, it could potentially mildew. It sure is a bummer, when this kind of thing happens, and I hope it works out well for you.
Since we're here, I'll share something about glazing. (If you already know this, sorry for the repeat.) Basically, glass and acrylic have two levels of protection. Regular filters about 40% of UV light, whereas conservation filters 99%. Anything can fade over time, and not just from that extra UV. Heat can cause fading, as can all the other light in the spectrum. The quality of the media also affects fade. If art on paper uses a pigment-based media, it lasts better. If it lacks pigment, (i.e. a dye-based ink, or low-quality watercolor), it is prone to fading. It's likely that this frame had regular quality glazing, so if you keep it, it'll last longer if kept out of sunlight. Also, away from fluorescent lights. If you have anything that you'd like to protect as well as possible, custom frame shops have conservation glazing. It comes in clear, which has good detail and reflections, as well as museum finish. Museum is not for steamy bathrooms or kitchens, as the finish is more delicate. It costs more, but is wonderful, because it has very few reflections. And lastly, if you ever want to super protect something from moisture, find a framer who uses MarvelSeal. They can hide that inside the fitting, so humidity doesn't get in. Thanks for taking time to read this, and wishing you a lovely May!