My air pump is gone. Can I remove the bracket (pictured) as well or is it part of something else?

 

Figured it out. The bracket can be removed. No need to reinstall the bolts as they only hold the air pump bracket. There is also another small bracket on top that can be removed but the nuts have to be reinstalled because they hold the alternator or its bracket (it is V6 engine).

 

Yep, just had to take mine off while doing a front cover gasket, didn't even think to put them back on and it's been fine. Just have to tie back one wire & connector that was tucked back there so it's not flopping around trying to get caught in the belt.