I'm a bit confused. Are you asking whether to seed the area with grass, or what to use as a mulch after seeding?

Any newly seeded area that gets much foot/dog traffic isn't going to do well. It will get bumpy, and there will be lots of scattered bare patches. i've never used the mats you refer to, but a local landscape company puts down a thick layer of straw when they seed in similar circumstances, and seems to get acceptable results.

If the dogs run in that area, covering the seed won't help. You'll need to keep the dogs away from that area until the grass is established (probably next spring).

Well, so much for that idea. Thanks for the replies. I can't keep them off of it because of the logistics -- it's why my backyard is crabgrass. The previous owners took terrible care of it and with 7 special needs dogs I can't just fence off the yard. One of them leaps like a gazelle and would just go in anyway. I guess I'll just let the crabgrass fill it in.

We discovered that the front lawn has some sandburr plants. Isn't that just lovely?