How do I remove an incorrect parking lot label?

(assuming it was and is still a private car park) then I wouldn't remove it - I'm guessing someone's added it based on aerial imagery, and if you just remove it another mapper could easily add it back again. Instead, I'd add an "access=private" tag to it so that anyone looking for a car park won't park in it by accident. On the "standard" OSM map the "P" shows in a dimmer blue; applications looking for car parks are able to look at the "access" tag and warn users away from private ones.

Here is an example of a private parking area near the Pennine Way that I marked as private for exactly that reason - there's a sign beside it saying "private", presumably because tourists were using the owners' spaces and leaving them with nowhere to park.

Of course; if it's not somewhere that cars are parked then just delete it from the map, or retag it as what the current use is (with "access=private" if appropriate, of course).