Since TML leaves most hooks intact, I suspect Ban Hammer will work without problem. Did you try it yet?
Otherwise, simple hook into the registration_errors filter
https://codex.www.ads-software.com/Plugin_API/Filter_Reference/registration_errors
For example, put this in functions.php (it’s untested):
function disallow_banned_email_domains( $errors, $sanitized_user_login, $user_email ) {
$blacklist = [
'binkmail.com',
'bobmail.info',
'chammy.info',
'devnullmail.com',
'letthemeatspam.com',
'mailinater.com',
'mailinator.net',
'mailinator2.com',
'notmailinator.com',
'reallymymail.com',
'reconmail.com',
'safetymail.info',
'sendspamhere.com',
'sogetthis.com',
'spambooger.com',
'spamherelots.com',
'spamhereplease.com',
'spamthisplease.com',
'streetwisemail.com',
'suremail.info',
'thisisnotmyrealemail.com',
'tradermail.info',
'veryrealemail.com',
'zippymail.info',
];
list($name, $domain) = explode( '@', $user_email );
if ( in_array( $domain, $blacklist ) ) {
$errors->add( 'blacklisted_email', __( '<strong>ERROR</strong>: Your email has been banned.', 'my_textdomain' ) );
}
return $errors;
}
add_filter( 'registration_errors', 'disallow_banned_email_domains', 10, 3 );
Don’t forget this is a arms race you will lose in the end if someone really really wants to register with a disposable e-mail address!