MSY TRACON Controller reported MVA obstruction no longer exists and facility failure to update display resulted in an inaccurate low altitude alert.

Narrative

Aircraft X departed HUM on a heading of 050 to avoid weather. The aircraft remained on this heading until clear of weather then proceeded to destination airport. Unfortunately when making this turn it placed the new route over an MVA of 3;000 ft. for an antenna. I did not catch this and the aircraft overflew the antenna and the Low Altitude alert sounded; upon realizing that the aircraft was in this location; I issued a turn and a climb; then a low altitude alert. I was not exactly in a big hurry or very eager to protect this MVA due to the fact that the obstruction does not exist and has not existed for nearly a year. It was destroyed by Hurricane Ida and our facility has done nothing to reflect that change on the STARS display or terrain systems. We are protecting an antenna that is not there. I broke the 'rule' but the rule is not reflecting reality. The pilot even said the antenna was not there when I turned him. STARS maps need to be updated to reflect the absence of an increased MVA requirement in this area. If there is no obstruction; why are we increasing our workload and irritating pilots by making them stay away from something that does not exist. I messed up by the fact that I understand we are required to protect it at this time and did not notice it; but also it has been basically removed from my mind as it doesn't exist.