It would be interesting to take some of these GAN demos and write a utility where for each output, have it find the closest-matching training input, and see how similar it is.
To answer this one would need to invest time into researching something that might potentially deflate the AI hype, so no one is doing it. Training dataset similarity analysis I usually see in these papers is downright laughable.
I don't think GAN work that way (I haven't followed it last year though). My understanding is that a GAN simply tries to determine if an image is generated or authentic. I suppose they used one there.
One way to do what you propose would be to plot all the training pictures in the kernel space of the autoencoder and match the closest one to the generated picture.