How important is it to glue/adhere the battery again when replacing it? I swapped out the battery and closed it up before considering that I should have used adhesives. Will this be a problem and should I go back in and open the phone again to secure the battery?

Question: What is that black covering under the battery in the battery compartment area? I scratched it up somewhat when removing the adhesive from the battery (huge pain) and want to know if this will be a problem. Is there something I can do to repair the black covering if I need to?

What is that black cover under the battery? I scratched it but am unsure if that is important or not.