The jewelry though is really pretty and you have not only earrings but the matching brooch. Probablly goes for more as a matching set. And it’s signed.
I would think it is just a print. So not a fake - but just a nice, mass produced print suitable for framing. But that said - I would set it aside before you toss it. I think you could start by bringing it into any art/antique store to get their opinion. Just giving it a quick google, I see this image a lot as a print but not in this color palette, so that’s kind of interesting. If you google “Two Harlequins Book of the Month Club” this image comes up, but it’s painted with deeper colors. No numbers on it anywhere that say 15/500 to show it’s a limited edition print? I think it’s neat!
A closer inspection of the back, not the drawing itself, but what was behind it (if I understand her correctly), has this:
I don’t think it’s a fake per se, but if there’s any indentation probably a print. All the water damage will not help with the value and Picasso was extremely prolific. In good condition it would be worth hundreds not thousands of dollars.