Help a newb here, please

How can one move Grin between exchanges? For example Poloniex<->Bittrex

It is recommended that you withdraw to your own wallet first, in case of transactions not going through. That way you do not have to deal with two support channels at once.

Otherwise, transactions with exchanges work just like normal transactions. If the exchanges both support the same type of transactions, you can just be the MITM.

As far as I can tell, you can’t move funds between the two. Why?
Is there a wallet with GUI ?

Yes. Grin++

There’s also Niffler wallet. I’ve done what you’re trying to do with that one - link below: