What year car is your photos? The 67-69 OEM boot is not supposed to go between the seat and side. And there are no snaps on the inside where I see one on yours, that I have ever seen.
I have a 69 GT. Assumed boot was original...? As you can see- it slides nicely between seat and back panel and snaps securely with 2 snaps on each side. One on top of panel and one on side of panel.