Apple ignores the dot or period in Gmail addresses?

So, apparently Apple and Gmail do not have the same opinion about "dots" in email addresses. Gmail ignores them, Apple does not.

I have a problem where I get notifications to my main email account "jane(dot)doe (@) gmail (dot) com" for someone logging into my iCloud account "janedoe (@) gmail (dot) com.

I proceed to change my password to the icloud account associated with the "dot" gmail address.

I log in, everything is fine.

I try to log into icloud using the "janedoe" address to no avail - the password does not work. So, I click "forgot password" and it cues me to type in my phone number. The numbers provided are definitely NOT my phone number. The account without the "dot" is definitely not my account. HOWEVER, I keep getting all of their notifications through to my Gmail account, because of course, Gmail treats the two as the same person.

Is there a work around for this?? How do I even attempt to fix getting notified about an account that is not mine, but is mine according to Gmail?