Whenever there's an update, the updater will recognize that SourceTree is still running and offer to close that automatically, but later on it will complain about Putty.

Tracing the process ID back to the task manager, led me to the pageant.exe inside SourceTree's program folder. Killing that process allowed me to continue the update's installer.

The problem reoccurs on every new update.

It would be nice if the installer could take care of this tool as well so that I wouldn't have to kill it manually every time.