I just replace the tee unless I am having a water problem. I use a hacksaw to cut through the tee where it doesn’t cut the pipe. Then I sweat the cut tee off of the pipe. If you have a dry system then there is no problem in resoldering.
However heat causes moist air to expand and will attract water remaining in the pipe. If you can get two ends of the piping open by opening faucets then you stand a chance.
If not then I will solder two pipes into the tee and a 6″ or one foot pup. I will then solder a coupling on the one piece of pipe. When you get the pipe and fitting up to temperature try not to increase the heat any more. It won’t hurt to have a compression coupling on hand so that you can get back in service if you do have trouble soldering.