You say the floors are continuous but there’s also a gap? Continuous as in one piece or as in its the same flooring from one room to another? If there is a break in the flooring I’d use a transition piece to avoid a dirty crevice

What type of flooring is it?

@Donald sorry, I meant the new floors continue into the next room with no break in the pattern, so there's technically no need for a transition strip. The small gap is in the old linoleum beneath, because the old floors had a transition strip there. It's pretty small, but I'd still be concerned about it maybe forming a crack there over time.

@millworkman it's just vinyl.

No transition strip is a better look.

Some floors require the transition strip at doorways or pinch points. Yours being square "should" be ok but I would double check if you want the product warranty. And definitely fix the crack under the vinyl.

I can fill the crack but it may still be just a little lumpy around that area. I didn't think vinyl tile needs space in doorways for expanding and contracting, but I'll look into it.

I'm seeing 'peeling paper' on the floor. Are these peel and stick tiles? If they are, there is no need for a transition strip. I agree you should patch that bit through the doorway.

Only floating floors require the transition strip. If these are 'fixed' by adhesive then there is no need for it...other than to deal with large gaps or holes that are too large to patch/span.

Yeah, it's just peel and stick. I patched the area. We'll see how smooth it is. If it's a little uneven I'll cut it and put a strip. I just don't want this to happen:

The previous owners put a peel and stick floor in the bathroom without removing a few inches of the previous flooring. Who knows why.

Fill the strip, and make sure its very level. Then put the tiles back down. No transition strip. Your wife is right on this one. :-))