There's a simple way to this in any C-like language. The style is not Pythonic but works with pure Python:
def remove_html_markup(s):
tag = False
quote = False
out = ""
for c in s:
if c == '<' and not quote:
tag = True
elif c == '>' and not quote:
tag = False
elif (c == '"' or c == "'") and tag:
quote = not quote
elif not tag:
out = out + c
return out
The idea based in a simple finite-state machine and is detailed explained here: http://youtu.be/2tu9LTDujbw
You can see it working here: http://youtu.be/HPkNPcYed9M?t=35s
PS - If you're interested in the class(about smart debugging with python) I give you a link: https://www.udacity.com/course/software-debugging--cs259. It's free!