What is the ruling on forgetting to convey the greeting entrusted to me by an acquaintance, and what is the authenticity of the saying "A freeman's word is a debt" – is it a Hadith or a well-known proverb?

Conveying greetings is obligatory according to some scholars, such as the Shafi'is, especially if the messenger committed to it. Whoever deliberately fails to convey it is sinful, but if they forget, there is no sin upon them. The saying "A freeman's promise is a debt" is not a hadith. Fulfilling a promise is strongly recommended, and breaking it is severely disliked. Allah has condemned those who say what they do not do, and praised His Prophet Isma'il for being true to his promise. The Prophet considered breaking a promise to be one of the characteristics of hypocrisy.