Which claim? The full transcript of the Feynman story is available online [1], you can search for "martian" to get right to the story. It's presented in the context of explaining CP symmetry, which says that physics is conserved under a parity (mirror reflection) plus charge inversion (matter -> antimatter) transformation. Of course it's only approximate [2].

I got the quote slightly differently from what is recorded on the caltech sight, the one they have is

> So if our Martian is made of antimatter and we give him instructions to make this “right” handed model like us, it will, of course, come out the other way around. What would happen when, after much conversation back and forth, we each have taught the other to make space ships and we meet halfway in empty space? We have instructed each other on our traditions, and so forth, and the two of us come rushing out to shake hands. Well, if he puts out his left hand, watch out!

[1]: https://www.feynmanlectures.caltech.edu/I_52.html

[2]: https://en.wikipedia.org/wiki/CP_violation

The assertion that it is possible or the attribution to Feynman? Scientific American [1] references Feynman's 4th Messenger lecture at Cornell: "Symmetry in Physical Law" (1964) [2] [3]

[1] https://blogs.scientificamerican.com/degrees-of-freedom/gala...

[2] https://www.feynmanlectures.caltech.edu/messenger.html

[3] https://www.youtube.com/watch?v=W7K1kXeK-tY