I think there's a good chance it's genuine, but I haven't studied Rowling's autograph enough for you to buy it based on my opinion.
Can you get better images? Those are fuzzy. If that's what the seller's images look like then you want to be extra careful. If you do then you may get more valuable opinions than mine here.
I would rather not go into detail since the current Rowling forgers are improving by leaps and bounds. A very knowledgeable friend recently got taken by an extraordinarily convincing one on Ebay - even had me and veteran UK watchdog hp4u fooled until Peter Kenneth, aka The Potter Collector from Instagram tipped us off to the sellers patterns.
I will tell you that my opinion is based on observing her signatures over a 11 year span.
I have several signed first/first HP books but fall far short of being an expert. My first impression was consistent with Gregory’s. It isn’t real as it seems that the slopes/curvature is off. The attractive price/offer is a bit too good.
Here is an example of her signature authenticated by both autografica and psa/dna.