Andrew Miller sends this in: “This sounds like a reference to some phrase. ‘Friends with benefits’ is the only similar thing I can think of and would be a stretch at best. Also not sure why one dog has opposable thumbs and a smartphone. Is the joke just “fleas are contagious?” That would be less of a joke and more of a useful tip for a child that just discovered them.
Since I have space in the comment box and it’s come to mind, I’ll recite De Morgan’s Siphonaptera:
Great fleas have little fleas upon their backs to bite ’em,
And little fleas have lesser fleas, and so ad infinitum.
And the great fleas themselves, in turn, have greater fleas to go on;
While these again have greater still, and greater still, and so on.”
Comics I Don't Understand 
Though it is not a deep joke, I think it is indeed just playing off of “friends with benefits”. And the revised version, “friends with fleas”, is depicted literally.
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My first thought was Words With Friends, but that doesn’t seem to work as well.
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I find that the Six Chix artists tend to whatever they feel like doing and the syndicate is all good with it. I mean, if you don’t find it funny, clearly you hate women.
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It was good to see that Siphonaptera poem again, after many decades. As for the comic, I fear that ‘Friends with benefits’ is what Lawton mad in mind, and she was just sloppy about having one dog with hands and phone.
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