FTP Tool – Is There an FTP Tool That Can Search for a Phrase in All Files in a Directory?

An oldie, no key though.

http://www.archive.org/details/tucows_288687_Super_Ftp_Search

This looks promising http://www.wftpserver.com/ftprush.htm

From the ftp man page:

mdelete [remote-files] Delete the remote-files on the remote machine.

So you should be able to connect to your ftp server, navigate to the proper directory, and then mdelete the desired files:

ftp nobody@ftp.example.com
cd my_local_directory
prompt
mdelete *.txt~

The prompt command tells your ftp client not to ask you for a confirm each time.