I think I know the responses to this, but bear with me...

A customer picked up a cake on Saturday, then came back in on Sunday (I wasn't there on the Sunday) with about a quarter of the cake, complaining that it was underbaked. She had served the cake to her guests on Saturday night, but didn't eat any herself. She didn't mention that any guests made any comments or pushed their cake away.  Then she went to eat some of the cake on Sunday (who knows how it was stored overnight) and claims she found it underbaked.

So yes, this is insane, for so many reasons. I baked, filled and decorated the cake myself, so would have noticed if the layers were underbaked. It was also a cake with a lemon filling- so most likely the filling soaked into the cake layers, making them seem a little mushy when it was a day old. (And she's complaining about her day old cake!!) She claims she's done this exact thing with this cake flavour of ours before and it wasn't like this. My employee kept the leftover cake and I checked it out the next day and it seemed fine.

The customer wants me to call her back to discuss this and usually I have no problem calling someone, taking responsibility and apologizing if we made a mistake, offering a refund or replacement, even sometimes when we didn't really do anything wrong. But this is just beyond the pale. I cannot fathom what to say to her without being rude and am a bit horrified by the idea offering her anything based on the situation.

Anyone have any thoughts?

i'm thinking about it...

yeah I think i'd give her a 25% discount on the cake -- on the base price of the cake -- and let it go -- if she wants more tell her she served it to her guests so she got the usage of it -- done -- or bake her the size of the quarter cake she returned -- whichever is easier -- I would Not negotiate anything further though -- make your decision and stick to it -- but in there somewhere before you tell her your decision I would explain the issue with the filing -- 

it happens -- so sorry 

y'know what though -- when I cook berry filling I cook the phooey out of it so there is no water to leech out into the cake -- when I do lemon I know the eggs will hold it firm as well -- so you might want to recheck your recipe or if the filling is in a sleeve and check if it seems looser than usual -- idk -- just a stray thought

but I still wouldn't refund her more than that

It sounds like she might be wanting a refund   Most likely I would offer a discount on a next order since they have ordered before 

My first thought was the same as -K8memphis, refund for 1/4 the price of the base cake, not counting any additional charges for decorations.  Offer an apology to go with it and call it good.

Oh, and also as -K8memphis said, explain that there is a good possibility the filling made the cake seem underbaked after setting for a day.

and did it need to be kept cold? and did you remind her of that? -- just offering possible food for though for next time