I think the issue is that the only baggage claim at TBIT is the baggage claim at international arrivals which is a secure area. TBIT baggage claim is not set up for domestic arrivals.

Hence, AA routes the bag to T4.

As for the OP question, you can either exit landside at TBIT (although I don't think there is clear signage how) or just follow the signs to T4 and exit there.
The walk from TBIT to T4 is so short (whether walking landside or through the connector). Not a big deal.