It’s a common issue to have custom filter inputs outside of gridview that behave like gridview’s internal filter inputs that I see many people solved by keeping their filters on storage (eg session variable) but it would be an easy task if there was an attribute in gridview to change inputSelector default value in jquery.yiigridview.js
extending CGridView and adding this behavior is not a big deal but as it’s a simple change I think it would be better to be in CGridView itself
good luck