What do we do with our Blessed Palms?
Blessed palms - like holy water, brown scapulars, devotional medals, and so on - are "sacramentals," and while they do not convey grace in the objective way the seven Sacraments do, but, "by the Church's prayer, prepare us to receive grace and dispose us to cooperate with it" CCC 1670). As such, they may not be disposed of like common trash, but should be disposed of in a dignified way, usually by being burned or buried. It is traditional - and indeed it is our tradition - to burn those blessed palms and use the ashes for Ash Wednesday. So hang on to your palms, place them over a door or in some devotional nook of your home as an aid to prayer, and then bring them to Mass next Septuagesima Sunday (2/09/2020, but we'll remind you!), and you'll receive them back to help you remember that "thou art dust, and unto shalt thou return."