Here's how I accomplished this.

Create an FTP task. In the File Transfer set Operation to Receive Files and set RemotePath to *.* for all files or *.ext if you only want specific extension.

Then add a Foreach Loop to loop over the local directory to process the files.

After the Foreach Loop add another FTP task. In File Transfer set Operation to Delete remote files and set RemotePath to *.* to remove all files or *.ext to only remove a specific file type.