Mounting Acoustic Foam in a rented flat
I'm not sure how much weight this is, but if possible, I'd go with Command Adhesive strips. For example. (These are pretty common; just check Walmart or similar.) These are basically perfectly designed to avoid damage to rentals, and removal is simple. Each strip holds 4lb, so a quick weigh should tell you how many you'll need per foam piece. If you're worried about them attaching to the actual foam, remember that you can use more permenant methods to attach the strip to the foam. (Needle and thread could even create a mechanical attachment.)