Is the Hadith: "A gift is not to be rejected, nor given as a gift (by the recipient), nor sold," weak?

The phrase "تهادوا تحابوا" (Exchange gifts, and you will love each other) has not been reported as a Hadith; it appears to be a popular saying. However, there are Hadiths that encourage gift-giving, such as: "Exchange gifts, for indeed, a gift removes the rancor of the chest," and "Whoever is offered basil, let him not refuse it, for it is light to carry and pleasant in fragrance," and "If one of you is given a gift, let him not return it." These Hadiths indicate the desirability of exchanging gifts and the dislike of refusing some of them. It is permissible to sell them or gift them to others.