More than 25% of global sea level rise is caused by mass loss from the Greenland Ice Sheet. A significant part of this mass loss is attributed to interactions between Greenland's marine terminating glaciers and the surrounding warm ocean waters. The latter were identified as Atlantic-origin water masses recirculating in the Nordic Seas and the Eurasian Basin and intruding on the East Greenland continental shelf through systems of troughs. As the Atlantic-origin waters in the subpolar North Atlantic and in the Fram Strait are observed to be warming, a prevailing hypothesis is that this warming signal propagates to the glacier termina and contributes to the increasing ice melt. In this contribution, I will present results from a couple collaborative studies using backward simulations of Lagrangian particles deployed in warm waters close to three major East Greenland glaciers (Sermilik, Kangerdlugssuaq and Nioghalvfjerdsbrae) and integrated using output from high resolution ocean models. These lead to a common conclusion that the far-field warming signal in Atlantic waters is obliterated before it reaches Greenland glaciers due to multiple and crossing oceanic pathways, mixing with Polar Waters, and modulation of the inflow on the shelf by wind forcing. I will put these results in a broader perspective concerning the application of Lagrangian techniques to track warming signals over large distances, hoping to trigger a vivid discussion.