the only sure way to do this is to get a hammer, a very small cold chisel with a sharp mean little edje
and a can of WD 40.
by spraying down that lip is will loosen it up a tad. They you simply have to chisle and cut that lip all the way into the drain. you are making a cut through that brass flange or lip and it willl eventyally give , keep spraying the wd 40 into the gap if it doesent give, you just got to keep cutting into the drain.
and of course you want to chisel in the direction (counter clock wise) to persuade the flange to come loose.
the only real risk you take with any approach is chipping the tub near youir attack point. Try not to "dig down " into the metal underneath the tub....
try not to hit the tub with your hammer on your back swing either. (thats bad)
just get a small sharp chisel and keep it eating on the brass only.
the WD 40 is optional. but it seems to at least morally help.