From Mitch4:
He notes,
Huh? I can’t even identify the additional object next to the playing cards — nail clipper? cigarillo? — let alone what the dog is supposed to do with them to become more adoptable.
I think it’s a cigar–pretty sure that’s a cigar band in the middle of the object–but what do cards and cigars have to do with getting adopted?!
At the risk of being called mean, that strip bills itself as “REMIXED NEW YORKER CARTOON REJECTS”. I’d submit that if your cartoon is too obscure for TNY, you might have a problem!
Comics I Don't Understand 
I think it’s a reference to the “Dogs Playing Poker” painting.
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That seems likely, Mark, but I can’t figure out what that has to do with getting adopted.
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Some people think painting of dogs playing poker are cute, and cute gets dogs adopted.
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Already answered, but . . .
I always thought this was just a one-off kitschy painting, but as it turns out, it’s a whole series, and many were created to advertise for cigars.
https://en.wikipedia.org/wiki/Dogs_Playing_Poker
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I took it to mean, that the dog has these items for it’s owner, like the St. Bernards with the barrel of rum (which was not worn by avalanche dogs). But the cute angle works better, I suppose.
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Or, the dog is being gifted these items (a good card hand and a cigar) so he can fit in with the “dogs playing poker” series?
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Alll I could conjure was Triumph the Insult Comic Dog, who smokes a cigar and at least once hung out in Vegas.
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I was just trying to figure out the stupid “Giant symbols of the 4 suits” cards, which could never be used to actually play poker.
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