Technical Help

I have a little technical question, hoping some WordPress wiz can help me with. Is there a way to remove all signs of commenting on WP “pages” (not to be confused with regular posts). I know you can turn of commenting on them, but you still get something like this:

I want to get rid of this completely, but obviously still allow commenting on regular posts.

Update: I should add that I have tried using the “if (is_page)” or the “if (is_post)” tags, but without success.