Is it necessary to re-wash the penis and testicles with the intention of purification from madhy (pre-ejaculatory fluid), if the intention was not present during the first washing?

The jurists have agreed that the intention (niyyah) is not a condition for removing impurity from the body, clothing, or other things. The place becomes pure upon the removal of the impurity, whether it is done by the accountable person or by other than his action.