Monzo don’t charge a conversion rate. This would’ve been applied by the ATM, not Monzo. My best guess is that you selected (or were tricked into selecting) ‘yes’ when the ATM asked if you would like dynamic currency conversion applied.
As @eden says, a lot of ATMs make their menu screens confusing, because the best case for them is that you use Dynamic Currency Conversion. I recommend that you use the in-app chat to alert Monzo to the fact that you did not mean to carry out the transaction in GBP, and to ask them how you could dispute this.
To be clear, they can’t help you directly; the error (as it were) isn’t with them. But they may be able to help you direct your complaint to the owner of the ATM used.
Alternatively, maybe some Turkish users will be able to chip in with replies to this thread.
As a Turkish person here, I’m surprised at the amount of money the ATM let you take out (I’m from the UK) the last time I went to Turkey the ATM’s only let me take out around 200TL. Maybe you should try to go to the Garanti branch you withdrew from and ask if they could do anything.