I thought those were mainly for PR application/citizenship application not for temporary permits but I could be wrong.
From what I know about the process, it needs to be due to an egregious mistake, new evidence or H&C grounds and submitted soon after the refusal. It is then at the discretion of the officer to review his decision (does not have to) and I believe tends to be done within weeks (the case must be pretty strong therefore shouldn't take 4 months). With COVID it could take longer and it is such a specific and niche situation I am not familiar with. I'd recommend not hanging too much on this, IRCC recommends either reapplying or filing in court:
Can I appeal a decision on a work permit application?
Under Canada's Immigration and Refugee Protection Act, there is no formal right of appeal on temporary resident decisions. Instead, you can reapply. If possible, a different officer will examine the application.
You can also ask for a judicial review through the Federal Court of Canada, if you think the process was not fair. A lawyer in Canada would act on your behalf.
I do not want to be too negative about it but in my opinion (and it is just an opinion) this is more of a way for consultants to get more money with a very low chance of success in most circumstances.