How to remove existing background color of text when highlighting?

Tags have priority. Tags with a high priority have preference over those that have a lower priority. When you select a range of text it is given the tag "sel". You simply need to raise the priority of the "sel" tag to be above the priority of your "match" tag:

w.tag_raise("sel")

Alex Martelli writes in the comments "it will do the OP absoluely [sic] no good if he sets highlightbackground instead of selectbackground" but that is incorrect. While he is correct that setting highlightbackground has nothing to do with the selection, it has no bearing on this solution.

Raising the priority of the "sel" tag works with the code in the original question, with or without the addition of the code that sets highlightbackground.

For more information on the text widget check out the text widget tutorial on tkdocs.com. It has code examples in Tcl, Python, Ruby and Perl.

I think you need to set selectbackground, not highlightbackground which means something completely different (the bg color for the "highlight rectangle" drawn around a widget when it gets focus). However, I believe the sel pseudo-tag (representing the selection, which is what I think you're calling "the highlight") is "below" user-created tags such as your match; if so, then the bg color for the user-created tag would show, not the bg color for the sel pseudo-tag (aka selectbackground).

With Tk 8.5 you could remedy that by binding to the <Selection> pseudo-event a function that places an appropriately colored user tag "on top" of pseudo-tag sel; however, there is no such event in Tk 8.4, which is what most likely you're using today. TK's docs say that 8.5 comes with Python 3.1 on the ActiveState distribution of Python for Windows; unfortunately there are only "TODO" placeholders regarding other platforms or other versions of Python -- I don't know how to best obtain Tk 8.5 for the specific platform(s) and python version(s) of your interest.