Thomas is correct. They have been blessed and the proper way to take care of them would be to burn or return them to the ground.
Most churches will purchase their ashes instead of burning their old palms. But a few years ago my parish forgot to purchase them, so I began the tradition of burning the palms again. It makes for a nice close to ordinary time and the teens and the altar server enjoy it because they get to participate. It is one of the few times that the servers are able to lead the community in prayer at my parish.
But with that said, it is not easy to burn palms. They burn easy enough. But they do not render down well unless they burn pretty hot. They also burn with a very strong smell that does not easily clear. So if you plan to burn, do so outside and be prepared to take a shower and wash your clothes soon after because the smell stays with you.
So the best option is to dig a hole in your garden and place them there to help the soil. They will not sprout palm trees.
God bless and enjoy living your faith every day.