At the top of the script:
read LASTDATE < .last_date

During the FTP session:
del $LASTDATE.backup.sql.enc.gz

After the FTP session:
echo $DATE > .last_date

Of course you will need some conditional logic there to deal with .last_date not existing... you could create the first .last_date file manually yourself. If you need help with that as well let us know.