  In a noise driving by a multivariate point process $\mu$ with predictable
compensator $\nu$, we prove existence and uniqueness of the reflected backward
stochastic differential equation's solution with a lower obstacle
$(\xi_{t})_{t\in[0,T]}$ which is assumed to be right upper-semicontinuous but
not necessarily right-continuous process and a Lipschitz driver $f$. The result
is established by using Mertens decomposition of optional strong (but not
necessarily right continuous) super-martingales, an appropriate generalization
of It\^{o}'s formula due to Gal'chouk and Lenglart and some tools from optimal
stopping theory. A comparison theorem for this type of equations is given.
