How can I stop output from within a script.

I have 2 scripts. Script A calls script B. In script B, I start a tail in the background. After processing, I stop the tail at the end of script B. However, I get the message such and such process was killed. It doesn't seem to be coming from the tail or the kill command. The only way I can stop the message is to redirect B's output to /dev/null. I want to stop it in script B.

Any ideas?

I assume you're doing something like:
kill $pid

Change that to:
exec > /dev/null 2>&1
kill $pid