Basement sliding glass window (Pella) – how to remove the pane opposite of the sash

Is it DIYable? Yes. No. Maybe?

You may find that you start the job, everything works out just right, and you complete the work in record time and under budget. More likely, you'll run into a bunch of unforeseen problems, take 5 times as long as you'd expect, and end up way over budget.

The best way to tackle DIY work that you are not sure about, is to have the resources available to quickly fix mistakes. In your situation, it might be a good idea to purchase a replacement window before you begin. If you damage the old window beyond repair, you'll simply have to install the new one. On the other hand, if the repair works out, you can return the new window you purchased.

It also never hurts to have somebody with knowledge in the type of work you're doing, so if you run into trouble they can offer guidance.

If you come across something you are really not comfortable with, there are always professionals available to do the work for you. You might also be surprised that they charge less than you might think (not always the case, but does happen).

I'm guessing, but here's my suspicion based on the pics posted. I may delete this answer after you post an updated close up pic.

Where your red arrow points - the white and black strip - I suspect that's the stop strip. It goes all the way around the window panel and appears to lock it in place. I suspect there's one on the outside as well.

To remove the glass, you're probably going to need to carefully remove this strip from the outside of the door frame. Then the window pane itself should lift up and out from the bottom.

To re-secure your new pet door will include re-installing the stop strip.