Any ideas on how to attach carpet to pack of DCSB rear seats?

I'm trying to think of a good way to attach some scrap carpet I have to the back of my DCSB rear seats, has anyone seen this done or done it themselves?

The motivation is my 4-legged friend. I like to keep the rear seats hair-free, but when she stands on the hard plastic of the folded-down seats, she slides all around. If I take a corner too fast, she ends up on the other side of the truck.

I have some scrap carpet lying around, but I'm struggling to think of a way to attach it without damaging the seats. Glue was a thought, but I feel like it would end up a huge mess (and a pain if I ever needed to remove). Velcro might work, but I'm not 100% sure it would hold her standing on it. I haven't really had any other thoughts, but I'm open to anything you'll throw at me!

Edit: I meant back, not pack! Not sure how to change title.

 

PM CoTacoTRD on here. He has 2 german shepherds and has done something like this to his seats.

 

Thanks for the tip! PM sent