Anti-theft system

If they found the correct keys, it should work. As far as your other question, if that light is flashing, I hate to say it but it will need to go to a dealer to have it reprogrammed it will cost about $130.00. And no, there is no way to bypass it. The only thing that will bypass it (if it is still functional) is turning the key to the run position and allowing the vehicle to sit like that. After about 10 minutes, the light should go off and the vehicle should start.

This guide should help

https://www.2carpros.com/articles/how-to-reset-a-security-system

Please run down these guides and report back.

The switches that control the lights for open doors are made right into the door latches and they have a history of sticking and causing problems like that.

Here is a technique that often works well and eliminates the problem at no cost.

Get a can of spray lube like WD40 or something like it and has a straw on the nozzle. Spray it generously up into the latch mechanism. Now open and close the door numerous times to work it in. Repeat this process several times. Since you don't really know which door is causing the problem, you should do all of them. It's usually caused by the most frequently used door but it's not guaranteed to be that one.

What happens is the switch in the drivers door latch goes out then the system thinks the car is getting stolen.

Here is a guide to replace the latch and fix the problem. (below)

You will need to remove the door panel first.

https://www.2carpros.com/articles/door-panel-removal

Testing from the book if needed:

TEST C - DISARMING ANTI-THEFT
Arm system. Warning indicator should be on. Press UNLOCK button on remote transmitter. Observe doors. If system disarmed and warning indicator went out, go to next step. If doors did not unlock, repair remote entry power door lock circuit. If system did not disarm, go to TEST E. If doors unlocked, but system did not disarm, call telephone number on RAP for assistance.
Arm system. Warning indicator should be on. Unlock driver's door with key. Repeat procedure for passenger's door and liftgate. If system disarmed and warning indicator went out, and vehicle is not equipped with driver's door keypad, system is okay. If system disarmed and warning indicator went out, and vehicle is equipped with driver's door keypad, go to next step. If doors did not unlock, repair door locks. If system did not disarm, go to step 5).
Arm system. Warning indicator should be on. Attempt to unlock doors with keypad. If doors unlocked and system disarmed, go to next step. If doors did not unlock, repair remote entry door lock circuit. If doors unlocked, but system did not disarm, call telephone number on RAP for assistance.
Enter RAP, PID/DATA. Select IGN_RAP. Turn ignition off. NGS tester communication may lost be after a few seconds. IGN_RAP state OFF should be displayed. Turn ignition on. IGN_RAP state RUN/AC should be displayed. If displays are as specified, disarm circuit is okay. If displays are not as specified, repair defective ignition switch circuitry, or replace defective ignition switch. See Fig. 1.
Enter RAP, PID/DATA. Select DR_DARM. DR_DARM NOT ACT should be displayed. Unlock each door and liftgate with key. DR_DARM ACTIVE should be displayed. If NGS tester displays both states, call telephone number on RAP for assistance. If both states are not displayed, inspect all switches and associated wiring for shorts or opens. Repair as necessary, then retest system.

Please let us know what happens so it will help others.

Cheers, Ken