You don't want to pull healthy plants out, but if you mean that you don't want to KILL healthy plants, take some and separate their roots from their twins and re-pot them. Many people do that all the time and have great success. Size is an issue, though, so don't wait too long.

Every sort of plant has a suggested spacing from others. It's not
chiseled in stone but it's a rule of thumb that one ignores only at
peril unless one is experimenting or knows a whole awful lot. So in a
way you can say that the tom seedlings are healthy but they won't stay
that way without some serious work. 99%+ of gardeners wouldn't plant them
out while so doubled and tripled up.

Yeah, normally tomatoes are grown in clusters :) so those needed to be transplanted to individual containers some time back. This assuming you want most of them to survive.

If you don't then just snip all the extras off and then transplant the remaining ones into a larger containers individual 4" containers - they are already rootbound in those 72 cells as those are intended for germination but not growing-on.

It's going to be very difficult to separate the root balls now without doing damage but you should be able to save most.

For future reference the term "thinning" normally applies to direct-seeded vegetables, not those grown as transplants. So while it is possible to germinate several tomato seeds in the same cell you cannot grow healthy multiples in the same cell.

And when you transplant those to the new containers be sure to plant them deeply burying most all of the bare stem.

Dave