Found the answer on stackoverflow.
;; Disable the system cursor caused by screen reader etc.
(setq w32-use-visible-system-caret nil)
Helps to know that you need to search for "caret" instead of "cursor".
You could change the face (colour style) that is hard to read:
Alternative foreground color, a string. This is
like :foreground but the color is only used as a foreground when the
background color is near to the foreground that would have been used.
This is useful for example when marking text (i.e., the region face).