Have you tried this with smaller PDF files to see if the size is an issue?
Have you tried deleting with ExecuteSQL instead of the relationship?
I'm using small file sizes (300 to 800KB). Also, I did some research this morning into deleting via ExecuteSQL, and it seems that I would need to install a driver to set FileMaker as an ODBC data source. I am hosting this database on a server that is accessed by several people outside our office, and can't install anything on their computers.
You should not need the OBDC driver unless your files are in a completely different database or on a different server. If you did you only need the driver on the server as far as I know.
It looks like your table is local in the screen shot and you can use ExecuteSQL right off with no drivers. It is a native script step. I would suggest giving it a try.
I use ExecuteSQL from a remote location all the time no driver needed.