I’ve done it on computers and cell phones, and I assume the pump would be similar. There’s no seams or screws on the body, so it must be accessed by removing the screen with the help of a heat gun, a suction cup, and a playing card or spudger. There are plenty of videos on YouTube showing you how to do this on a phone, you won’t find anything on a t:slim in particular. I have absolutely no idea what the pump looks like inside, but electronic connections usually snap together like Legos in things like this, so I imagine it wouldn’t be too difficult to figure out.
The problem is, you can’t just buy the replacement part off of eBay. Where would you get a new battery to put in it? Tandem certainly wouldn’t sell you parts, it would be too big of a liability. You’d have to buy someone else’s old pump to strip it for parts, and then risk possible damage to both while attempting the repair. You might as well just buy a used, but still functioning one and use it instead. Maybe Tandem will do out-of-warranty repairs for a reasonable cost? I really don’t know.