You can turn off the Tick marks with the TickDir property on the GeographicAxes:
geoplot(42+rand(10,1), -71+rand(10,1))
ax=gca;
ax.TickDir='none';
(note: on older MATLAB's you had to instead set the TickLength property to [0 0])
To remove the tick labels (and the marks along with them), you have to drill down into the Latitude and Longitude axis:
geoplot(42+rand(10,1), -71+rand(10,1))
ax.LatitudeAxis.TickValues=[];
ax.LongitudeAxis.TickValues=[];
I'm less sure about turning off the labels, I think they just come with the basemap?
