Woah, pump the brakes, that's a bit extreme!
Here's the thing -
unless you specifically ask for a document that has all of those details, nobody actually gives them by default.
I speak from experience; when I filed my application back in 2016, I had to ask all my former employers to give me a letter exactly like the one the CIC expected to outline what I did to meet the requirements, but it was Plan A. I had a backup plan to use based on what I saw via research on these very forums.
Here's an example going back to 2013!
Plan B is simple - you keep the standard reference letter they gave you, keep your pay stubs (and make sure you get those for the period you were paid), your original offer letter and if you aren't including it already, your bank statements to show the salary for that period being credited to your account.
Remember: You are not lying about your experience in Company E, so you have nothing to hide and everything to gain by providing as much evidence of your work as possible, even if Company E is not being particularly cooperative. To be honest, most Indian companies would make it unnecessarily difficult too (it was for me, too!)
Do not take or think of such drastic steps to withdraw your application over things like this! Everything's going to be fine.