In a noise driving by a multivariate point process $μ$ with predictable compensator $ν$, we prove existence and uniqueness of the reflected backward stochastic differential equation's solution with a lower obstacle $(ξ_{t})_{t\in[0,T]}$ 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 Itô'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.