How do I take a list and remove it from a file?

grep -Fxf list -v /etc/remotedomains > remotedomains.new
mv remotedomains.new /etc/remotedomains

The -v tells grep to only output lines that don't match the pattern.

The -f list tells grep to read the patterns from the file list.

The -F tells grep to interpret the patterns as plain strings, not regular expressions (so you won't run into trouble with regex meta-characters).

The -x tells grep to match the whole line, e.g. if there's a pattern foo that should only remove the line foo, not the line foobar or barfoo.