  In this article, we study the squarefree powers of facet ideals associated
with simplicial trees. Specifically, we examine the linearity of their minimal
free resolution and their regularity. Additionally, we investigate when the
first syzygy module of squarefree powers of a simplicial tree is linearly
related. Finally, we provide a combinatorial formula for the regularity of the
squarefree powers of $t$-path ideals of path graphs.
