Several controls that look identical do completely different things, and one of them refuses to touch a camera-written location at all. Here is how to clear the location and confirm it is gone.
A photo carries three blocks of metadata and most of two of them are yours to change. Here is the working subset: each tag, what it holds, why you would touch it, and what reads it.
WordPress does not strip the location out of the photo you upload, but the copy your visitors download may have lost it. Which happens comes down to one setting.
Windows will show a photo's location but will not let you add one, and the Mac Photos app can accept a location that never reaches the exported file. Here is what each actually does, and the browser route that avoids both.
The coordinates are already inside the file. Here is how to read them out, why the number arrives without its minus sign, and which tags tell you whether the location is a measurement or a guess.
Google's photo uploader has no location field, so a geotag has to go into the file before it leaves your computer. Here is how to put it there, and what three published tests say it will and will not do.