My 2007 TSX sat for 5 months and battery died. I took out the battery to have it charged, and I noticed this piece was loose and flopping around. (No bolts present.) Looks like some sort of cover?

Replaced fully-charged battery and started my car up fine. Drove it for like a block before I got an exhaust warning. Could this cover thing being off cause that error? Any other ideas?

Thanks in advance for any advice/opinions/suggestions!

That's a cover for the engine air inlet. You need some plastic push-pins to secure it.
It shouldn't case any kind of error.

Item 12: https://www.acurapartsforless.com/v-...onator-chamber

If your follow the opening you should be able to see that it leads to where your air filter goes & past that into the throttle body.

I know this only bc mine is just sitting there without the plastic push in clips just like yours. I noticed it after sitting a jump starter there and the piece just kinda fell off when I picked up the jump starter. I've just sat it back in place every time I've knocked it off while messing around under the hood & it's always still in place whenever i open the hood. Even got hit in a wreck that crushed my driver side bumper right in front of where this part sits and it was still in place without anything holding it on.

That piece is def not the reason for your malfunction indicator. Have you gotten the code pulled yet? If not you can stop by practically any auto parts store & they'll read the codes for free.