Search this view capability which was added in the product with 2020 Release Wave 1, searches on the fields specified in quick find view, but takes into consideration the selected view definition, when performing the search.
This is enabled by default.
Here Search this view will perform the search within the selected view i.e. All Contacts in this case.
The results show 3 records found within the All Contacts view, for the search term “alex”
The same search term returns blank in the case of Inactive contacts is selected.
The same applies to the sub-grids
To turn off this, select Yes for Use quick find view of an entity for searching on grid and sub-grids from General tab of System Settings
After applying the above change, we can see the text renamed to Quick Find within the Search Box.
Searching now, irrespective of the view selected, will perform the search across the records as per the definition of Quick Find view.
More on it
https://docs.microsoft.com/en-us/powerapps/user/grid-filters#use-search-on-a-grid
Also read – Search limit on Quick Find
https://docs.microsoft.com/en-us/powerapps/user/grid-filters#use-search-on-a-grid
Hope it helps..
Nishant Rana's Weblog 
Reblogged this on Phani Rajasekhar.
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hi Nishant,
How can you disable that search box completely? I want to remove the search functionality from the table.
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We cannot hide the Search this view option on Grid, the only supported way of not allowing user to search is by removing the Find Columns from the Quick Find View (it would need at least one field so select a particular field which has no value or not used)
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