Telegram Basics
Official telegram.org Source
Yes. You can always delete any messages yousentorreceivedforboth sidesinanyone-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 forforwarded 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.
Official Telegram Reference: https://telegram.org/faq
Part of the TGWAY.com Official Telegram Knowledge Base (98 Verified Q&As).