What is the ruling on a woman responding to a man on social media with the phrase "Jazakallahu Khairan" (May Allah reward you with goodness) when he posts a supplication or a Hadith? Is she sinful for doing that?

There is no harm in this word, but it is necessary to be cautious about correspondence between non-mahram (definition) men and women without need, in order to block the means (to sin). Likewise, a Muslim woman should avoid entering mixed websites and forums, as this is further from suspicion and safer from temptation, along with the necessity of being cautious about the dangers of the internet in general.