Chemgal sends this in: “I feel like I’m going to “get” this Barney and Clyde, but at the moment I don’t. I do get that Grandpa is misunderstanding which “hit” is intended, but is that the whole joke? If so, I guess I should be submitting this as an “OY!” rather than as a CIDU.”
Seems obscure enough for a CIDU.
Comics I Don't Understand 
I think if “touché” had been spelled correctly it might have helped.
beckoningchasm, I think the line is from Hamlet.
I think the joke, if there is any, comes from the use of the word “hit”. In Hamlet 5.2, it’s used of a sword blow. It’s an entirely different context in music.
Mark H, I took “touch” to be a fencing reference, too, but that didn’t make it a pun to me, and I couldn’t make the music thing make sense, either?!
As Rob W and Mark H point out, part of the line is an almost exact quote from the duel scene at the ending of Hamlet. It’s spoken by Osric, a minor character who is acting as referee for a supposedly friendly but actually deadly match between Hamlet and Laertes (who has some pretty legit beefs against Hamlet, if you look at his side of the story).
So “hit” and “touch” in that original are both about scoring points in fencing. The robo-dog knows this and knows that he is quoting; but Grandpa Pillsbury does not know, and makes an unconscious pun taking “hit” to mean “success”. (As has been noted, he apparently doesn’t do anything punny with “touch” .)
So if you’re intent on exactly quoting the Shakespeare, then I would have left out the “Touch”, because it will only confuse the issue, as everyone will expect “Touché”. So then we’re left with the dog’s response to the criticism as being “A hit, a very palpable hit.” meaning he takes the criticism (ie: “Touché!”); Grampa misinterprets what he says as further descriptions of the topic, to which the dog says, “nobody appreciates my puns” — only, either there isn’t a pun, just a statement conceding the previous accusation, or else, if he meant a pun with “hit”, then Grampa getting confused with the meaning of hit is really the ultimate appreciation of a poor pun as you could hope for…
Furthermore, the dog singing a song to Grampa in the fictional setting (and not in the meta setting of him being in a nationally syndicated cartoon) would not entail copyright infringement, as this is as fair a fair use as fair could be — we are all allowed to sing any song we want, as long as we’re not doing it for a large audience as part of a commercial performance with no educational or satirical purpose.
The basic joke is just an AI dog being a smartass.
Touché, Mitch4 (5). You too, larK (6) and Downpuppy (7).
AI is famously incompetent so perhaps the joke is that there is no pun, just nonsense.
I thought it was ‘AI getting the word “Touchè” wrong, because, ha ha, AI gets things wrong.’