that's usually what i had to do once the center broke out. i would cit a slit in an easy to get to spot mostly through then stick a screwdriver in the slot and the strainer would usually snap the rest of the way. depends on if it's cast or stamped.
Careful not to cut into the tub. You may have better luck with a hacksaw blade. Cut a slit in it then insert a cold chisel in the slip and rap it in the direction you would to unscrew it (counterclockwise) and it should loosen up. You could start with some WD-40 or penetrating oil.
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