If your local water is hard, the haze may be calcium carbonate buildup. In that case, adding an acid to the vessel may clear up the deposits. I suggest distilled vinegar or 88% lactic acid as options. StarSan is also a good acid. You should be able to add a small amount and swirl instead of having to fill the vessel.
If that doesn't do it, then the glass may be getting etched by something like a strong cleanser.