The narration in the question is authentic . It has been reported by Imam al-Bukhari in his Ṣaḥīḥ and also by Imam al-Tirmidhi in his Jāmiʿ. Therefore, quoting and attributing this Hadith to the Prophet ﷺ is correct.
The content of this narration reflects the humility (tawāḍuʿ) and simplicity of the Prophet ﷺ. It also encourages Muslims to accept invitations and gifts, even if they are small, as doing so strengthens mutual love and respect.
*Brief Explanation:*
The word “kurāʿ (كراع)” mentioned in the Hadith has been interpreted by the majority of Muhaddithīn as referring to a sheep’s trotter (a very simple and modest food item). The meaning is that even if such an ordinary item is offered as a gift or invitation, it should be accepted, as accepting a Muslim’s invitation or gift is an act of virtue.
However, some explaners of Hadith have interpreted “kurāʿ” as referring to “Kurāʿ al-Ghamīm”, a Famous place between Makkah and Madinah. According to this view meaning that even if the place of invitation is far away, one should still try to attend—provided there is no valid reson of excuse—in order to honor and please a fellow Muslim.