We were advised that because our DSL is coming thru a separate data
line, there would be no need to install phone filters on the
individual phones. However, even when everything was working OK
(which is not the case at present) there has been static. Sometimes
it was mild but other times it was terrible. Whenever, I pulled the
DSL wall insert from the jack, the static cleared.

I had a normally operating phone system first, then the ISP guys came in to
fine tune the system as I was getting some drop off with the computer..
They fiddled around a while and everything works fine now. I asked if they
put in a "filter" and they said no.

BTW, our ISP company provides phone support AND FREE home visits if that's
what it takes.
IMO (and theirs) its their responsibility to make sure you get satisfactiry
service/connection

Give yours a call and ask if they do the same..if so, let their guys worry
about getting it fixed properly.