Is it permissible to take the item for free from the seller after he pledged to that effect if it is found at a cheaper price elsewhere?

The prevalent aspect in this article is the enticement of the customer to buy, rather than a genuine gift. If the seller offers you an item out of courtesy and fear of disgrace, and his soul is not content, then it is not permissible to take it, and it must be returned. However, if the seller intends a genuine gift and his soul is content with giving it, then there is no harm in taking it, because the criterion is the contentment of the giver's soul, as the Prophet, peace and blessings be upon him, said: "It is not lawful to take a Muslim's property except with his full consent."