Mum's friends are still letting her know the "gossip" of their social circle, which she's misinterpreting. Is a group email appropriate to address this?

Yes! Explain briefly and tell them mum likes to hear about positive things like where they just had lunch or how the hollyhocks are doing. That sort of discussion will leave her with happier things to think about, especially if she thinks she did them. It might be helpful to tell her friends that mum really doesn’t know who they are talking about now and may be only pretending to be interested in the gossip.

That's nice that her friends still call. If your mom takes on their complaints as her own, how is it difficult? Just annoying for you? I'm sure it is, but OTOH, is it really a big deal? Maybe just let her run with it? Answer vaguely (oh, that's too bad mom) and change the subject?

Do her friends realize that she has dementia? If not, that might be a group email to just make sure they realize what's going on. I gave a few of my mom's good friends a heads up so they would know what to expect when they did connect and to understand why they weren't hearing back from her as it is difficult for her to followup and to use technology.

Good luck!

How is it difficult?
Does she cry and worry what will happen to her or is she just wanting to talk about it and you want to avoid the subject? If it is the later, I would skip to what GM54 said and move onto something more pleasant.

My experience has been that what I tried to control was more about my own anxiety than my aunts.

Once a friend told her about obscene phone calls the friend had received. Aunt started talking about the calls as if they had happened to her. I knew she had dementia but I didn’t yet know that how I reacted would influence her mood and absorption of any situation. I was busy telling her that no it didn’t happen to her and I didn’t want to talk about it. I turned it into a memory she tucked into the part of the brain where dirty words are stored. If you haven’t met that one yet, you will be amazed at what will come out of the mouth of someone you have never even heard say dang. I decided that if she didn’t repeat it, maybe she wouldn’t remember it. Didn’t work. She learned not to say it to me but years later newer care takers would tell me that she told them about the time she got the obscene calls.
Then I got upset about people calling her up or dropping in to tell her about a recent death in the family. I would be so angry at the thoughtless person for upsetting her. The truth was she forgot it as they went out the door.
I think as long as a person lives within a community narrative and let’s hope that’s a long time, there will be news, good and bad, they will be exposed to. Depending on her dementia and how fast it moves, chances are that window will close and she will go on to other difficult to understand behaviors. I would be more afraid the friends would stop calling or behave differently with her and as you said, she lights up when she hears from them.

I just want to add that each person with dementia is different. You will find what works for you. The dementia patient is usually fairly forgiving of our mistakes as they are truly off into their own world.

Is there one that is the "head" of this clique? If so I would ask that person to see if she can not keep the conversation away from health matters. This might be difficult as it seems to be a topic of high priority whenever friends gather, does not matter the age of the group either. I find myself doing the same when I get together with friends that I see but 4 or so times a year. It is just another level of "catching up"
You might not be able to stop it but you can try to find different ways to contend with the aftermath. Maybe be more positive about her health. "Gee, that is to bad about Betty, good thing you don't have__________!
Or if there is someplace she loves to go you can say to her "Mom, after Betty and the girls leave, if you are feeling well we can go get an ice cream (or whatever she likes)" That will give her positive reinforcement to not let the bad stuff effect her physically and mentally.
Some of this may or may not work depending on her dementia. She may not retain what your comments are. If that is the case then it might be a matter of just "riding out" the aftermath.