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.
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?