Here’s my take on this, as recovering specific app data can be tricky.
Recovering Telegram messages directly from an Android device after a few days is challenging. Because Telegram is cloud-based, when you delete a message, the instruction is sent to their servers. Your local device cache then syncs to reflect that deletion, often overwriting the old data.
You could try checking Android’s Notification History if it was enabled; it might have captured snippets of the messages. Some general file recovery apps claim to work, but their success with encrypted app data like Telegram’s is not guaranteed.
Looking forward, this is where a cell phone monitoring tool becomes relevant. While it can’t retrieve what’s already gone, having one installed acts as a preventative backup, logging messages as they arrive. It’s less of a recovery tool and more of a proactive data-saving solution.