Will this tube fit this tyre?
 

I know tubes are pretty flexible WRT sizing but I just got 26*1.5 slicks for my wifes MTB and the tubes that were on her bike are labeled 26*1.75-2.35.

I mounted the tyres and all seems fine but is it right to use these tubes?

Right - no. The Patron Saint of bike part sales is cursing you right now.

Will it work - yes. Getting the tires on when using wider tubes in thinner tires can sometimes be an issue, but since you're obviously past that it should be fine.

At this point, I wouldn't "undo it".
In the future, if you have a flat, inspect for "fold" marks. IF it has any, I'd replace it at that time.

Tube sizing seems somewhat iffy. I've seen some marked similar to your size that needed to stretch noticeably just to reach the minimum (1.75)marked size and others that didn't.

My 26x1.5" tires have tubes marked 1.75x 2.1 and there was no problem.

Should be fine. My pops even uses 26" tubes on his 29er for years!

I don't use 26" tubes but I have (27") 700x28-32 tubes which are difficult to mount into my 700x28 wire-beaded road tires. It's easy to get the tube caught between the bead and the rim. If I use a 700x20-25 tube, though, mounting is pretty easy and there is little chance of pinching the tube. So, I'm going to err on the side of a smaller tube from now on.