As
@lazergeek stated the screen is the aerator inlet, the aerator outlet is the fitting that your red arrow points to, if you notice on the gunwale there is a little black circle that says air inlet which is the air pick up for the aerator.
You will not be able to gain access to this pump or fittings from the rear bilge area that is accessed under the clean out tray, I’ve been rather intimate with this area lately. However, since your boat is new and under warranty, with the boat dry and on the trailer you can just pull the pop off access hatch, fill the live well to the top and then look through that pop off hatch with a good flashlight. If there is a leak you will see it, and any water that leaks should start coming out the drain plug. If you can identify that there is a leak take it back to the dealer and let them fix it, that area is a tough area to work in, and the only way I can see gaining access to the aerator is by taking a lot of stuff apart that you shouldn’t have to.
Note: when you pull the pop off hatch off and look down in there you will see a pump, but that is the fill pump not the aerator pump that you suspect as leaking.
In your pic with your arm in it, that fitting is the overflow for the live well. The live well level will drop down dramatically if you have been “boating” with it full.
Hope that helps.
By the way, how did you get a 22’ fsh ?