That's strange, none of mine have ever eaten a wrap. I hold the battery parallel with the mod, seat the edge of the negative end partially against the raised area of the bottom contact and then slide the positive end in until its top contact is against the raised area of the top contact. Then I just push the battery straight in.
If you push one end of the battery in all the way and then try to force the other end in, I could see it tearing the wrap, especially on the negative end. Just try to keep the battery parallel with the mod as you press it in so the raised areas of the mod's contacts are touching the metal parts of the battery contacts only.
To remove, just pop off the door and spank the mod against your opposite palm and the battery comes right out no problem.
I tried that slap to remove, tore the wrapper. Maybe they loosen up a bit with use, but I’ll just pull the bottle for now. Aside from that, I really like them.