Voltour, I don't know about Gmail but presumably Paymium and Kraken have your ID and can effectively attempt to verify your request.
GreenAddress on the other hand doesn't ask you for ID and can't disable two factor authentication from an unauthenticated request - if we were to do so there would be no point in two factor authentication in first place and if we were to disable 2FA for any bad actor trying to social engineer his access into a wallet you certainly wouldn't be happy.
As a matter of policy we do not remove/disable/change two factor authentication against unauthenticated requests.
We have no way of knowing the owner is you aside from authentication, which you enabled!
Two factor authentication is entirely optional (you can have 0 enabled or all 4) and allows to have multiple of them so that if one becomes temporarily or permanently unavailable you can use one of the other choices you pre-selected.
In your specific case you mention you used only Google Authenticator and seems that you didn't back up the initial seed as per two factor authentication instruction and you didn't enable email two factor nor email nlocktime (yes it is optional for privacy reasons and because you may not want to use 2of2 which is optional but use only 2of3 which is also optional)
For the time being my suggestion, with the above in context, is to keep backups of all you have (mnemonics, etc if anything) in case we can devise some solution in the future.