Hi sorry I was not clear, by other avenues I meant more permanent sponsorship. In that way most of the rights you have to enter as a Canadian can be inferred on to your spouse. The letter of sponsorship from your parents is really just an invitation letter, if push came to shove it cannot be legally enforced. This is more of a permanent solution so there's other factors that play into it like residency requirement etc.....so if this is not the solution all you can do is try for a trv and hope you get approved. Here is a link to spousal sponsorship.
https://www.canada.ca/en/immigration-refugees-citizenship/services/immigrate-canada/family-sponsorship/spouse-partner-children.html
I think others have already answered, they do not have concerns about where your spouse travelled or what they did there.....instead by travel history they mean they want to see travel to countries like usa uk Canada aus etc...it is a bit of a catch 22 because they wont give you a visa to travel but expect you to have travel history …..how can you get that travel history if they wont let you travel?!