In order to filter the RadGrid TemplateColumn you need to need to set the DataField property for the column to a valid data field from the data source. This ensures that the control properly retrieves the data on which the filtering pattern will be applied. Please go through the following demo which demonstrates filtering on GridTemplateColumn.
Grid / Filtering Template Columns
Please give it try and let me know if the issue still exists.
All the best,
the Telerik team