~snip~
No. You don't get my idea. I meant if you don't enter your email address on that site, they likely don't have your email address in their database. Maybe they have it on database or maybe not before the time you enter and search. It is only assumption and the prevention is protect the privacy of your important email address.
As same as when you use your bitcoin address, when you lost its anonymity, you can not get it back.
I agree with this. Curiosity killed the Cat. If you're really concerned that your e-mail address is compromised then the best idea would be to practice safety and change your e-mail to a new one and attach it to the places where it is important. Like Bank accounts, Online Exchanges, maybe Social-Media etc.
As soon as you enter your e-mail to above or any other site, they now have it and can use it for any purpose, if they wish to ie. So, even if after entering your e-mail to above mentioned sites you get the message that your e-mail is not compromised, or whatever message it shows. Make a new e-mail and change it places where it is necessary.
I am not sure but the best they can do when someone has your e-mail is try to guess your password through brute-force attack I assume. And as long as your password is strong it would be not easy to find it. Plus if you have 2fa enabled then that would be another layer of security that they'd have to bypass to get through. I remember watching Mr.Robot and Elliot had to install malware into someone's computer to gain access to their e-mail because they had 2fa enabled.