Cytotoxic t cells recognize and kill host cells infected by viruses. they recognize these cells by the foreign antigen displayed on the host cell's:

The statement above is TRUE. 
There are two types of T cells; cytotoxic T cells and helpers T cells. Cytotoxic T cells are specialists in killing cells that are infected with virus or some other pathogens. T cells are antigen-specific  and they defend the body against infections. T cells have the capacity to eliminate pathogens that reside inside the host cells.