Chloe Fineman ’s brushing off her NYC restaurant boot for saying "hi" to Demi Moore ... and it’s all thanks to the actress herself swooping in with a personal reach-out after the chaos!

Check it out ... we ran into the 'SNL' star in NYC Thursday, and she spilled that Demi slid into her DMs first following the incident ... and the two had a sweet little back-and-forth!

You gotta peep the full clip ... Chloe gushes over Demi and says she’s feeling way better about that restaurant boot, which she first detailed in an earlier TikTok.

Chloe said it all went down at Sant Ambroeus, when she and her sister Emma spotted Demi with her pup, Pilaf the Little Mouse, at a nearby table, and casually said "hi" ... even reminding her they’d crossed paths before. Play video content

But the manag

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