The lack of Canadian large scale military participation was due to practicality and not moral objections to the invasion [1]:
"The weakness of the Canadian military had been a factor in its very limited role in the 1991 Gulf War. While the military had been asked about the feasibility of sending 4 Canadian Mechanized Brigade Group (4 CMBG) from Germany to the Gulf to participate in direct combat operations, the Canadian Forces were forced to report that Operation "Broadsword", a theoretical deployment, would likely be a failure."
[0] https://www.cbc.ca/news/politics/weston-canada-offered-to-ai...
I have no connection to Iraq personally.
I do not collectively harbor guilt and constantly stress about the horrible things that the country I choose to reside in has done in their past.
I have Hong Kong products in my house, and I interact with people who were born in Hong Kong all the time.
The same cannot be said for Iraqi products or people.
That is the point I am trying to make.
I try to keep up with the military involvement of my country, I'd guess other people in other countries would do the same.
Tho I guess in contrast to you I actually get to interact with a whole bunch of Iraqis, Afghanis, Syrians, and other nationalities out of the MENA region.
People out of HK are a rather non-existing sight at the local refugee reception center.
Canada very reluctantly helped the US with their air raid campaign over Afghanistan, but as far as I am aware we didn't have much say in Iraq.
And either way, I fail to see how that translates to having a closer relationship with their people.
If anything, it distances them from our psyche.
Obviously the invasion of Iraq was the wrong thing to do. I am not arguing that it was right in any way whatsoever.