I figured it out. Seems I only need to set the marker of the children in the plot. The Code I used
% --- Executes on selection change in lines_or_points.
function lines_or_points_Callback(hObject, eventdata, handles)
all_child_handles_axes_eis=get(handles.axes_eis,'Children');
all_child_handles_axes_drt=get(handles.axes_drt,'Children');
switch get(handles.lines_or_points, 'Value');
case 1 %LINES
set(all_child_handles_axes_eis(1:end), 'Marker', 'none')
set(all_child_handles_axes_drt(1:end), 'Marker', 'none')
case 2 %POINTS
set(all_child_handles_axes_eis(1:end), 'Marker', '.')
set(all_child_handles_axes_drt(1:end), 'Marker', '.')
end