I lived in the eastern Sierra for several years, and climbed Telescope when the trailhead to Mahogany Flats would be opened by the Park Service. According to my hiking logs, I did Telescope in mid-May consistently. Was it snow-free by then - the first few miles of the trail was usually clear by that time, with a patch of snow shortly after the col between between Rogers and Bennet as it's shaded and passes thru trees. That section is mostly flat, so no issues even if people aren't familiar with snow travel. The last 1K' of elevation is usually snow-covered, however, and the safest route is to follow the ridge straight up the slope rather than attempting the trail. As it's north-facing, it might present problems on the ascent, but it usually soft on the return. I usually carry crampons, and have sometimes worn them on the ascent.
So ... if snow/ice is an issue for your friends, perhaps early to mid-June would be a good estimate for snow-free travel.
Hope this helps.