The dialog needs a standard X to close the window. I get this at the most random times and I have to go in circles force quitting the app, messing with settings or restarting the computer.
If BTT is still working, then you are running into a macOS bug.
In this case sometimes only a reinstall of macOS helps to completely fix this.
However you can try this command to disable the message from BTT, some functionality might stop working randomly though:
defaults write com.hegenberg.BetterTouchTool BTTDisableAcccessibilityCheck YES
same here, alert message box BTT would like to access data from another apps keep showing. its stoped when I delete BTT app