It appears the threaded hole is in the latch. Since the latch is being replaced anyway, I’d guess the easiest method is what Nevada suggests above, just drill the bolt head off. Worse case thehole in the door gets a little enlarged, that’s what washers are for.
If that approach is not viable for OP’s specific situation for some reason, maybe not possible to position drill, and all else fails, I’ve had success for that sort of stubborn screw to just grab hold of it end-on w/vice grips, then put a screwdriver between the jaws to twist it out. Filing/dremmel’ing a couple of flats first would make that job a little easier. A dose of rust-busting thread penetrant (Liquid Wrench/PB Blaster) the day before is worthwhile too.