My girlfriend [22F] got hit on by a guy while we were on holiday. He asked for her email and she gave it to him, without mentioning that she has a boyfriend [me 23M]. How would you react?

So it's really not a complicated story. We were working together abroad (we didn't meet on holiday, we went on a working/holiday trip together). This guy was your classic music geek, and without being rude I wasn't and am not the slightest bit threatened by her and him. He lives in another country and she clearly had no interest in him in any romantic form.

My question is more based on the president set. Basically, she was friendly to him and he played her some music (in front of a lot of people they didn't hang out alone). Then he requested to meet her and she went down and he asked if they could stay in touch and if he could have her email. She told him she was leaving the country soon but didn't mention having a boyfriend and gave him her email. I understand she sees it as no issue as she has no interest in him whatsoever but to me it sets a bad tone and she's kind of inviting interest, and I guess my main concern is someone at home would do it and she'd react the same way. How would you feel about all this and would you do the same to your partner?

TLDR A 'geeky' guy asked my girlfriend for her number/email, she gave him her email without mentioning she had a boyfriend. Would you see that as a big deal or as her simply trying to be nice? How would you react?