If you sprayed Windex directly on the screen .. . I would immediately rinse with a micro fiber cloth and lots of distilled water over and over again. Maybe add a bit of isopropl to it.
A lot depends on the screen surface material. If the screen has any kind of plastic filter material, diffuser, or such on it; Windex will probably eventually yellow the area it was sprayed on. Particularly if it is any sort of acrylic carbonate or something like it. How do I know this? From several years of working on TVs from RPTV, DLP, LCD, etc.
If, on the other hand, the screen surface happen to be glass, or some form other of plastic it may be ok. But the yellowing I mentioned is not evident right away. It would show up only have weeks or months as a smeary haze that gets more pronounced.
Oh, there is a new type of Windex that does not contain ammonia. It will say something like. "Safe for tinted auto glass" or Safe for all mirrors". It contains no ammonia but does contain a certain amount of ethylene glycol. Will that affect the plastic on a TV screen? Hard to say.