If you went to court, IMNSHO, she probably wouldn’t get alimony. Both parties are entitled to ask for it, though (I think).
However, it may simply be cheaper to pay her off than to spend the money on attorney’s fees for a court hearing or extended negotiations.
$600.00 (and don’t forget, this is an above-the-line tax deduction for you!) comes out to four (give or take) or fewer hours of attorney’s time, and a court hearing (or possibly extended negotiations) would almost certainly exceed that…
If my STBX said something like that, I’d be asking where do I sign? (The STBX has already chewed up enough my money in attorney’s fees…)
Although this does depend on what her income is, what your disability is, whether your disability is temporary or permanent (and how much any extra care for your disability costs. If temporary, how long before you return to work? (If it’s permanent, and she’s currently making more, she might be required to pay you alimony if you both went to court…)
IMNSHO, if she’s talked to an attorney, it would probably be advisable for you to do so, as well.