You're not unreasonable in wanting it to stop at all. It sounds awful. Who's having fun here, honestly?
I concur with previous posters that you can't have your children being upset like this. I understand that your mum will throw the most unbelievable tantrum if you try to ask her to stop, and you will be the worst daughter in the world, and she just thought it would be a bit of fun and now you personally have ruined it forever specifically because you hate her and want her to be unhappy. (My mum is also the centre of the universe, and also needs my children to win at everything. One of them can't even walk and she's already inadequate.)
The thing is, you can't make everyone happy here. Who would you rather being upset: your mum or your children? That's the choice.
You can say "No more quizzes". You really can. Your mum can throw all her toys out of the pram and call you mean names and get your dad to tell you off and tell everyone she meets on the street what a meanie you are when she just wanted to bond with her grandchildren over their superior intellectual achievements.
I told my mum during lockdown to stop hinting at being allowed to come over (like it was just me being a bit meanie spoilsport, not the literal law) until it was allowed again, especially on video calls with my young son because it confused him. It took three emails and many tantrums. But I did it. She lived.
Don't even phrase it as a question. If she likes to hold you hostage on the phone, send an email. Totally unemotional. Just tell her the fact: "Dear Mum, I don't think the children are finding the quizzes very fun, so please would you stop sending them. Lots of love, me."
Then set up an email filter so her reply is automarked as read and archived. Don't read it for a while, maybe ever. Don't reply. What else is there to say? Block her phone number for a few days, or make sure your phone doesn't ring for it. If she does it again, just send the exact same email in the exact same words again. Lockdown is your gift right now, assuming you're not using her for childcare. She starts a quiz? Hang up the Zoom call. Always have an exit plan to just leave. Quiz = no more grandchildren until next time.
DO NOT Justify, Argue, Defend or Explain. (Look up "JADE") Just tell her the fact: no more quizzes, thanks. Have a completely normal relationship with her...except that quizzes (or tantrums about them) = bye! speak soon!
After a quiz-based fiasco (because it will happen), give yourself a timer to be upset about it and vent to your husband/a friend, then put it away and act like it never happened.
But you also need to take this up with your children. Tell them that you know they hate the quizzes. You hate the quizzes too. They are a stupid idea and not at all fun and have nothing to do with how much you love them or their worth as a human being. Tell them they are not to do the quizzes. Tell them that if granny mentions the quizzes, you will hang up/leave. Tell them that if you are not there and granny mentions the quizzes, they are to say "No thanks!" and either keep saying that until you arrive or, if possible, go and get you. You will take the fallout, but they are not to do any quizzes ever again. That way, at the very least your children will know that you totally have their back on this so they don't need to feel bad about themselves.
All of this probably feels pant-wettingly scary. I nearly threw up one time I was so stressed about my mother ignoring my requests to not ask to come round when it wasn't allowed. (She's getting vaccinated next week so I just KNOW it will all start up again. Ugh.) But you can do it! The hardest thing is just sending the short email and then NOT doing anything. NOT reacting, NOT explaining, NOT getting into a discussion about it.