No, telescope won't damage your eyes, unless you are doing something that you shouldn't, like aiming your telescope directly towards the sun and trying to observe it.

Can telescope hurt your eyes?

A telescope will not hurt your eyes unless you observe the Sun without proper filters. Even solar viewing, like during an eclipse, is safe if you use an appropriate and high-quality solar filter. You may find other celestial objects (like the full moon) a little uncomfortably bright, but they are not dangerous.

Is a telescope dangerous?

But there can be danger too. Many telescopes across the world are large, with ever larger ones planned or underway, but they can also be exposed to extreme elements like storm or fire, or can at times suffer catastrophic structural failure.