The availability of a thermodynamic system with respect to an environment is the maximum work, which can be gained from bringing it into equilibrium with its environment by a reversible process. If the process has to proceed in finite time, there will be unavoidable losses diminishing the availability; this consequence is captured by the Finite-Time Availability. Here we consider the consequences of an availability extracting process for a paradigmatic quantum system, the parametric harmonic oscillator. Differences and similarities between its Quantum Finite-Time Availability and the classical Finite-Time Availability of an ideal gas in a cylinder with a piston are discussed.