Yes. You can always delete any messages you sent or received for both sides in any one-on-one conversation (in groups, it’s still your own messages only). You can also clear the entire chat history on both ends. On Telegram, deleted messages do not leave a mark in the chat.
Together with privacy settings for forwarded messages, this makes exchanging Telegram messages similar to talking face to face (without a tape recorder). As a result, users no longer need to worry about the data accumulating in their chats over the years. Both parties in a conversation have full control over what does and what doesn’t belong to their online identity.