There's a key off battery drain, with multiple suspects.
I don't have an FSM, so can't tell you what is normal range for the 2004.
It is enough you wouldn't want to leave the vehicle for months without disconnecting the battery or pulling the power off fuse.
Take a look at this, and pull the fuse and see if it resolves it.
Jeep Grand Cherokee WJ - Fuses
Unless the mechanic is an electrical system professional, you might want to consider
seeing one, as there are multiple checks you would want to make as far as voltage drops to ground from the - post on the battery with and without the alternator, drops across all the ground and + voltage cables, alternator open diodes, price/quality of battery, ability of battery to hold a charge under drain conditions, etc.
Dirty wiring and grounds are almost obligatory on an older jeep... and they can be anywhere.