We are building a log query module.
There is a date parameter and we configured TI parameter type=date in UX.
It is working and sending the value to TM1 successfully.
but the format of date is a bit weird:
pDateFrom: Fri Jan 01 2021 00:00:00 GMT+0300 (GMT+03:00)
can we manipulate how UX is sending parameter value to TM1?
Better to have something like: 2021-03-12
Of course a date dimension can be used but UX date type is better 
There is no special logic in the UX for supporting the date type. All we do is accepting any valid html input type as is (see full list here: HTML Input Types (w3schools.com) ). You could try to transform the date string in your TI or populate an alias on your date dimension that matches the format. Please be aware though that the format for the date will depend on the locale of the client computer.
We will add more sophisticated support for additional input types at some stage but for the time being they only do what the standard html input type does.