It's your cabin air filter should be a couple of tabs you push then take it out. I can't imagine how dirty it will be but your air flow will improve dramatically, the longer it has been in there. You should get another as if you leave it out it could get your AC evaporator somewhat clogged up and that will take a lot of time to correct.

 

If possible do you have any resources you could point me towards to find the tabs? I looked for about half an hour and had no luck with removing it

 

According to this 2002 Corolla No Cabin Filter?, you don’t have a cabin air filter.

 

According to this 2002 Corolla No Cabin Filter?, you don’t have a cabin air filter.

It looks pretty clean in that area for a 2002, don't you think? I'm wondering if the blower motor might've been replaced before. Or maybe it's just kept immaculate. I suppose there's some people out there who do it lol

 

If the videos I watched, shows 2003 - 2008 with the door between the blower motor and the foam section in op’s first post.

The one video that resembled a 8th gen, the filter is under the hvac assembly. Link that I provided says otherwise. Op, check under the heater core to see if the cover is there.

 

Filters were available only from the next gen I believe... so 2003. 2002 and below had no replaceable filters.

 

8th gens dont have a filter period. When I did the fan motor that piece of foam was fine but of course had seen better days.

If you feel the system is moldy etc, I'd run some toyota ac cleaner if your feeling fancy or lysol/soapy water to clean out the system (its not a permanent fix, and have to do it twice a year). You can also practice turning off the ac, max heat before you arrive at your destination to prevent mold formation, but honestly whose got mental space for that regimen.