No need for the if, just remove any files that match the pattern.

bin/backup.sh

@@ -18,10 +18,8 @@ time="`which time`"
 ## Main ##
 
 # Remove the last backup.
-if [[ -e "$BASENAME"*"$TAG"* ]]; then
-	echo "`date` - Removing existing file."
-	rm -fv "$BASENAME"*"$TAG"*
-fi
+echo "`date` - Removing existing files."
+rm -fv "$BASENAME"*"$TAG"*
 
 echo -e "\n`date` - Take down services for a cold backup."
 manage.sh -d