There are two ways in which earthquakes could affect the Antarctic ice sheet, either by occurring on the Antarctic continent or by occurring elsewhere and sending tsunami-type waves towards the ice sheet/continent.
Seismic activity occurs all the time on Antarctica. Particularly the West-Antarctic Ice Sheet (WAIS) is located over seismically active zones although such occur under the East Antarctic Ice Sheet (EAIS) as well. In the case of WAIS, subglacial volcanoes have been inferred from geophysical measurements. It is possible that such activity but also elevated geothermal heat fluxes, typical of seismically active areas, contribute to making the subglacial thermal regime temperate (at the melting temperature). This means the ice flow can, at least partially decouple from the bed and slide causing larger ice fluxes. Such behaviour is known from WAIS but is observed to be a part of the dynamic setup of the ice sheet and does not seem to change fluxes on time frames that we can observe directly or through investigations of indirect evidence of past flow variations. In short, there is no clear evidence that seismic activity in Antarctica directly causes major changes in ice loss.
Tsunamis reaching Antarctica could conceivably cause break off of larger ice bergs or larger numbers of ice bergs at the fringes of the ice sheet. Ice berg calving in Antarctica is largely through ice shelves, which are floating parts of the ice sheet. These ice shelves are part of the natural way in which the ice sheet looses mass so a momentary acceleration due to tsunami-type waves is conceivable. But, the main question will be of this momentary acceleration of calving simply causes ice that would calve anyway within some period is shed more quickly resulting in a period of quiescence as the shelf recuperates and resumes normal "operations*. This is unclear because we are dealing with processes that have to be seen over long time spans. The loss of an immense ice berg, such as occasionally reported in media, may not have that much significance in the long-term.
There are studies indicating larger ice fluxes out from specific outlets in Antarctica. How these may be influenced by direct or indirect seismic activity has not been investigated. Ice in glaciers and ice sheets behaves plasticly, which means it can accommodate external forcing to some extent by plastic deformation, and also elastically. As an example, lake ice may bend when waves propagate in the underlying water but can also cause breakage under certain circumstances (wave amplitude and frequency). It is hence conceivable that increased breakage can occur if circumstances are just right but it is not at all clear that such activity would cause anything but momentary acceleration of processes that would be shadowed by the longer term trends caused by climatic forcing.