Sniffing back Vs Blowing

My 4 year old caught cold and she keeps sniffing back the mucus. My MIL keeps telling her to never sniff it back and infact when she's already in middle of the act (sniffing,) forces her to blow. My daughter knows to blow the mucus out and I asked her not to bother and just sniff it back when she's already doing it and use a kerchief when the mucus it right in the nose.

My MIL started laughing at me and urged my daughter to never ever sniff it back and always blow it out. I wanna know is it harmful to sniff it back according to science? I did try to search online but couldn't get a clear picture on it.

Really appreciate the responses. Thank you