Yes, they did respect one another. One of his university faculty had been criticizing the Union general rather harshly. 'Sir,' said Lee, 'if you ever presume again to speak disrespectfully of General Grant in my presence, either you or I will sever his connection with this University.'
The worst thing I can find that Lee said about Grant was during the war ...
'His [Grant's] talent and strategy consists in accumulating overwhelming numbers.'
The harshest was reserved for Sherman...
'I have never understood why General Sherman has been commended for that march, when the only question was whether he could feed his army by consuming all the people had to eat.'
The fact is Grant and Lee were a lot alike. Brave and controlled.