If Greirat dies during his pillaging travel in Irithyll, his ashes can be found on his body floating on a corner of the drainage ditch inhabited by several Sewer Centipedes.
Once Greirat is killed during his pillaging travel in Lothric Castle, his ashes can be found along the rooftops of the Grand Archives. Proceed past a congregation of Corvians in the open area after the library, and make a leap to the rooftop below, where Greirat's body lies.
The yield that Greirat's Ashes give are determined by what he is currently selling upon death, rather than by when his last pillaging journey was. Thus, if Greirat is selling items available from his second pillaging journey and has yet to embark on his third, killing him and giving his ashes to the Shrine Handmaid will cause her to sell the wares he would have discovered on his third journey.