I have no idea if people paid for it or not
Uhm. You should know if your game was sold.
Also, if you have name your own price, any price makes the buyer a owner of the game. Whatever you give out as paid content, will be accessible to them (even external links). Even if you later change the minimum price. Of course, if you leave it at name your own price, this does not matter.
What itch should fix is, that people cannot increase their donation level later. A new donation is a new donation. This gets important if there is tiered priced files. Like, pay what you want with extra files. Someone donating 2$ and later donating 8$ to get your 10$ bonus file will not get the bonus file.
Oh, and if you change the external link to not have the game anymore, prepare for angry customers. There is some guide or faq somewhere that basically says, you should make the game accessible, if it was purchased. For pure donation pay what you want games, that might be different. Just read the faq for clearer information.