The sphincter is just a small ring-shaped muscle at the very end of the teat canal.
If milk isnt pouring out when she lets down, then it is likely not damaged.
How about a fresh photo of the injury so we can get a clearer idea of what you are dealing with?
In my experience (30 years

of dairying) any cow that is dried up w/ mastitis
WILL come fresh with it. It does not just go away, even with dry treatment.
So, if you hope to save the quarter then it is going to take some effort.
Another week or 2 of milking while treating her shouldnt hurt her.
It is for her own good, afterall.
She is in such poor condition though, you may end up losing the quarter anyhow.
Is the infection responding to antibiotics?
The longer it is allowed to grow in the udder, the more scarring it will do.
Stay dilligent and good luck.