I mean the door to the backroom inside the Dr's office. Sorry I wasn't clear.
Coming back to specifically thank you,
@Poke_4_Life -- this was the only tip that worked, and completed it in last night's run.
Was a little unintuitive to use right trigger aim to bring up the feature to rob the back door or the register -- normally when you hit LT, you get the option to rob, and was hesitant to hit RT to aim as it usually ends up with me quick-firing on the guy (which indeed happened the first time I tried with the doctor -- good thing for manual save points!).
First attempt, I didn't kill the doctor before going into the room, and got into a delayed shootout with the woman in the room, ending up spending too much time in the room such that multiple law men swarmed in and outside the office.
I could see this was going to lead to a very costly bounty if I did manage to get out alive.
So started up the save point again, blew the doctor and everyone else inside away ASAP, had time to loot everything and everyone (including ammo box and safe), and only had to kill one lawman before escaping with bullets whizzing by my ears.
Ended up with a bounty of only $1.25 or $1.50 -- pretty awesome.
Solid adrenaline rush.
Is there a reason why "Rob the Doctor's office in Valentine" remains in your log after you complete it? I noticed this with some of the side companion missions in camp as well (i.e. when I give the Naval Compass to Pearson after he asks me for it, it still persists in the log too).