I'm looking for a mod that basically alters, if not simply drastically lowers, the amount of money a townie brings into the household when they move in.

I do have the "No20kHandout" mod, which prevents any Sim I move out to not have 20k money on hand, but it doesn't seem to do anything to affect any townies.

I've seen videos of someone moving a townie into their household, and one time the townie moved in with just over 2k Simoleons.
Another time, moving a different townie in brought a pop-up that asked if the townie should move in with the default or altered money.

I'm not sure what exactly this mod now is.
Is it part of the No20kHandout or is it perhaps part of the hacks you can create with Monique's Hacked Computer? I'd like to move more townies into my playable households, but getting handed so much money right away removes some fun for me and I don't want to have to manually remove money with the FamilyFunds cheat.

zzMoveInAssets_Decide might be the one you saw on the video.

Since you use no20khandouts, it might also be worth seeing whether putting one of Pescado's money orders in the townie inventory works. It might only work for moving to the family bin though.