Whenever you do been prompted about this stuff then its better to avoid and there are several ways for you to push through without compromising your account.
That's right, because it's already evidence that you are sending to an address that belongs to the gambling site, and if you lied, they would also know if they make an investigation on your account. Actually, they wouldn't know it right away, but that doesn't mean that if you were able to pass by lying, you won't face the consequences of your past actions.
Well, there is nothing you can do once they had investigated and proved that the fund that you send to this wallet comes from the gambling site, sometimes the gambling site wallet staff has been detected as a gambling site wallet. We should avoided this in the first place if you really want not to be freeze by them your account.