I completely understand the unwrapping and checking a present. Most likely I'd give it to her to avoid additional issues that may arise from not giving it to her and just say "sorry DD Lola had to go away but she left me this to give you".
Don't lie and add the "Lola's very sorry she couldn't be here because she really wanted to" an NPD mother/grandmother is never anywhere she doesn't want to be as you well know
. Your DD will sadly learn one way or the other what Lola's really like and how much she truly wants to be a part of her life instead of swooping in as super granny with presents rather then her presence.
I haven't had anything to do with my NPD mother for 5.5 years but this time of year I found mine would do things to play up the PLOMs (Poor Little Old Me) and make any event about her whether with her presence or lack of it, making sure it was well noted. (my birthday is the day before your DDs birthday so I know this well) and of course made the stories about the horrible DD I am and how big a martyr she is even greater.