I just tell Jax No, I'm not throwing it. She'll woof at me while backing up and throwing her head and staring at me for a few minutes. Do NOT give in! lol I know it's hard but once you tell her you aren't throwing it that's it, don't throw it.
However, I do let Jax have it. She can carry it around all she wants as long as she's not bothering me with it once I've let her know I"m done. She's snoozing on the ottoman right now with her egg tucked under her leg. Once she's clear that I'm done playing, it's not a problem.
And keep more than one of her favorite on hand. It's not a good time if it gets lost. She'll drive me nuts looking at the spot it's supposed to be and barking at me even though it's not there. This morning I looked under every piece of furniture looking for it with her thinking it was a good time to flop on my head and get her belly rubbed. Finally found it in a corner!
I think letting her have it is fine. Just don't let her bug you about playing with her all the time.