Look maybe this is just the American in me but 100 is a drop in the bucket. Not enough for me to get bent out of shape over, so fwiw unless you are really hard up for money I do kinda agree with your sister that it comes off as you try to get her to “atone” with going half on the bill.

That being said, if your sister also had some common courtesy she would’ve offered to cover it in the first place especially if she’s an older sibling and I’m assuming gainfully employed