Demi Lovato isn’t backing down in her diet food war with a frozen yogurt shop — she’s now warning the store about messing with her … but also walking back her comments a bit, saying she was having a really bad day.

The singer continued going back and forth with The Bigg Chill — the fro-yo shop she attacked Sunday for its placement of sugar-free items — by sending a DM to them, complaining about the “GUILT FREE” label on cookies in the store. TBC defended itself saying the pic was old.

Demi swatted back … insisting they carried another, similar “diet culture” cookie — and also warned TBC to stop fighting with her, and that they didn’t wanna mess with her. She even dropped the ol’ … “customer is always right” on ’em.

However, Demi’s apparently seen the some of the backlash against her, because she just went live on IG, and restated her initial complaint — her visit to TBC seriously triggered her eating disorder issues — but she hopes she’s opened a dialogue with TBC about relabeling some products.

She added that she had a very bad day and weekend afterward, and feels like she needs a mental health day. Demi apologized if it seems like she’s a big celeb using her power to take down a small biz.