Great question — answering as the UphillTech team:
https://www.cbsa-asfc.gc.ca/do-rb/offices-bureaux/658-eng.html This is the customs and immigration office, if you cross inside the park. (There is a highway border crossing along the east margin of the park, at Chief Mountain, that would be a perfectly suitable place to cross for certain.) If you are going to be hiking when you cross into Canada, it looks like you can submit to inspection here. You should call the boat operator (you'll be arriving by boat, it appears) to see if this is a problem, and to inquire about how to secure tickets. (I think they normally provide a round trip from Canada.) If you want to talk to Canada Border Services Agency to check first (and I recommend you do),...
Full answer by Jim MacKenzie: https://travel.stackexchange.com/a/106599 (CC BY-SA 3.0).
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