The source code of the sample from the second screenshot demonstrates how you can filter iGrid using its SearchAsType object.
First, you need to configure this object:
fGrid.SearchAsType.Mode = iGSearchAsTypeMode.Filter;
fGrid.SearchAsType.MatchRule = iGMatchRule.Contains;
fGrid.SearchAsType.SearchCol = fGrid.Cols[1];
Then, set the text to search in the event handler of the TextChanged event of your filter box:
fGrid.SearchAsType.SearchText = myText;