This seems to have solved itself, but I when writing my previous post, I did see two PT 7.5 windows on screen at the same time. I closed one, and double-clicked the PT desktop shortcut: no warning, but there were two windows again.
Don’t know whether the fact that I installed 7.6 on that computer this morning made any difference. When I retested today, I had 7.6 closed, but 7.5 did give the warning on the second open.