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As I already mentioned, it doesn't matter how you were granted the PR.
This is the simplest way I can explain to you how your status changed over the years in Canada:

Out of status as a refugee claimant.

A convention refugee/protected person resident.

A permanent resident of Canada.

The RTD was issued to you because you are a refugee, not because you're a PR. Hence, don't use your home country's passport.
 
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My case is understood. My wife’s case is a bit different.

She was a child when she first came to Canada with her parents. Her family got to Canada through the UN & they received their PR confirmation upon arrival in the airport. Is she an immigrant? Or a refugee? Can she use her home country’s passport or she should apply for a travel document just like mine?
 
Hello, my mom and three brothers are convention refugees and they want to apply for Refugee Travel Document. They want to travel to Iran for a visit to meet family members who we haven’t seen for about 7 years now. Can they do that with RTD?

I want to go with them, I’m a PR who was granted PR through spousal sponsorship in Canada. How can I get a visa to Iran & go with my family?
is iran accept your visa on RTD