How to prevent rm from reporting that a file was not found?

-f is the correct flag, but for the test operator, not rm

[ -f "$THEFILE" ] && rm "$THEFILE"

this ensures that the file exists and is a regular file (not a directory, device node etc...)

Yes, -f is the most suitable option for this.

The main use of -f is to force the removal of files that would not be removed using rm by itself (as a special case, it "removes" non-existent files, thus suppressing the error message).

You can also just redirect the error message using

$ rm file.txt 2> /dev/null

(or your operating system's equivalent). You can check the value of $? immediately after calling rm to see if a file was actually removed or not.

\rm -f file will never report not found.