You do not have an implicit option to hide the search. And the suggestion which sureshqv provided will not work unfortunately as you cannot overlay objects in Sense.
Technically the search icon should be a cliff-icon. You will have to go with an extension to get rid of it. I am not asking you to create a table extension. You can create an extension to remove the search icon from the table I believe.
Not that this is always possible, but if it has not occurred to you, measures do not have the search option. In my scenario, I had a description of the main dimension so I made it a measure to remove the search capability and thus removed the spyglass.
If this is a requirement and the dimension has to exist, you would have to build the dimension in the load script so the displayed table has all unique values. By doing this, every column can be a measure and no spyglass.