Nah, it just users browser based javascript to push things around. I cannot say for 100% certain they don't nefariously save them, but they have years of credibility for not breeching trust on that front, so I really don't think they do, and there is no evidence in the console of the JS doing any kind of backend call to their side to stash anything it knows from your side.

Should be fine? No suing me if I am wrong some day!