How do you react if a team member is repeatedly late?

I would talk to them and explain why that behavior bothers me. 

It's important to emphasize that something like this shouldn't happen again in a professional setting. But we can't always know what might be going on at home for someone. I would suggest sitting down with her and trying to understand the reason for her tardiness.

First I'd try to talk to them personally to see if there's an underlying issue. If the problem continues I'd try to reinforce the importance of punctuality/reliability for our team's/the company's success and only if all of this fails I'd consider escalating the issue to a higher up.