Would that be "Dignum/Iustum est mundum reddere meliorem quam inventum/invenis"?
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For "it is right" I would use fas est. Literally this means "it is in accordance with divine law" (as opposed to human law), but in common use it just means "it is right/good/proper". It's typically linked up to an infinitive.
Reddere is not a bad choice for "leave"; it literally means to give something back, or give it up to someone else. In this case, you're presumably giving the world up to your descendants or humanity as a whole. Similarly, invenīre isn't a bad choice for "find".
So, all together:
Fas est mundum reddere meliorem inventō.
It is right to return the world in a better state than as it was found.
encouraged to upgrade from a comment:
Given the epigrammatic nature of mottoes, I wonder whether one needs to be explicit about either the fas or the world. What about simply “Redde meliorem”? It would fit better on the stone and make the viator think a bit.
Actually, now I think of it:
may be better.
The only problem I can see is that it could mean either “Give it back better [sc. than it was]” or “Give back the better one [sc. of the two]”, the latter being a bit of a red herring.
On the other hand, given that mottoes are a genre of crossword clue, I can’t see that this is a great defect. But I would be interested to hear which word order people think sounds more fitting for the intended meaning.