You are incorrect. The Inquisition was an instrument of the Church itself. In fact, its direct descendant, the Congregation for the Doctrine of the Faith, survives today as an office office within the Church, and was until 2005 headed by the future Pope Benedict XVI. The Inquisition's tribunals were entirely ecclesiastical, were conducted by priests, and under canon law.
It would be more accurate to say "the Inquisition targeted Jews who had been forced or coerced to have insincere conversions to Christianity on pain of death, exile, and/or abject poverty; it employed torture, and often handed over those Jews to secular authorities for execution."
A quick post before I retire but there were two different and distinct Inquisitions. It was the Roman Inquisition that was set up by the Church to combat the Albigensians in southern France. It never operated in Spain. The Spanish Inquisition was established by the Spanish crown and served the interests of the state, not those of the Church. Its attacks against the Conversos were a product of the state to eliminate those who were feared to be politically subversive; its purpose was not to target Jews to force their conversion. Failure to understand this distinction is a failure to understand history.