I mean the scenario when this domain in question (owned by OP) is used strictly for local business activity in Canada...
Well, I'm not aware of the domain name, how it is being used, or where this trademark registration application was allegedly filed. Perhaps I missed something in the brief comments posted by the OP, so we don't know whether we are talking about a USPTO application and a domain name used for strictly local business in Canada, or whether we are talking about a CIPO application.
Certainly, with a US trademark application, one does not "apply to fight the application" unless one is talking about a full-blown opposition proceeding, which is an administrative trial proceeding that certainly goes well beyond simply "I applied to fight the application".
What it sounds like to me is that the OP received one of those scam emails of a common variety in which the email claims that a trademark application has been filed somewhere, it has been spotted by the helpful sender of the email, and they will fight it for a fee of some sort. This is a very old scam, which pre-dates the internet.
But, hey, the OP has been offered the personal help of someone with zero experience in trademark disputes, and who said he didn't know what UDRP stood for until a few weeks ago. What could possibly go wrong?
I'm much more concerned that the OP is being taken in by a scam, than in any guesses as to whether there is, or is not, some reason for the OP to be concerned about a junior trademark registration application, wherever it might be. But the original poster doesn't seem particularly interested in reaching an informed answer.