This is a reference to the well-known idiom
the straw that broke the camel's back
A seemingly small or inconsequential issue, problem, or burden that proved to be the final catalyst in causing an overworked or overburdened person, system, organization, etc., to fail, give up, or collapse.
I was already fed up with my husband's lazy, selfish ways, but it was his refusal to get off the couch and come with me to my mother's funeral that was the straw that broke the camel's back!
With governmental resources already strained to the breaking point, any sort of environmental disaster would likely be the straw that broke the camel's back.
the straw that broke the camel's back
The final limit of capacity, including patience. An Arabian anecdote told of a camel whose owner loaded the beast of burden with as much straw as possible. Not satisfied with the staggering load he had put on the camel, the owner added just one last piece of straw. Even that one wisp was too much, and the animal collapsed with a broken back, leaving the owner with no way to take his goods to the market. The story is a parable for all the times you've been repeatedly irked until you can't take it anymore and you explode.
(TFD)
This usage of mind is roughly
mind
verb
with object
1.1 Object to.
‘what does that mean, if you don't mind my asking?’
‘do you mind if I have a cigarette?’
‘I wondered if he minded me reading them, and decided I didn't care.’
(Lexico)
Imagine the camel from the anecdote. It's lying on the ground with its back broken, and then the owner asks the camel, "Do you mind if I place another straw on your back?" (= If someone had asked [the camel] if he minded another straw [on his back].)
That's what it means. And whatever tone you imagine the camel using in that scenario, that is the tone in which Dennis replied. It's hard to say exactly, but perhaps annoyed disappointment, or stifled disappointment.
We can also see the idiom as a metaphor for the situation. It looks like something happened before that caused Dennis to feel disappointment. That thing is "the straw the broke that camel's back". Then Mona's statement ("Then I can marry Peter") appears to be "another straw", an additional thing that made matters worse for Dennis.