Cosmic rays propagate through the Galaxy and encounter systems that may trap them temporarily, as well as magnetic field structures that induce chaotic behavior on their trajectories. In particular, this is the case for particles that propagate in the local interstellar medium and interact with the heliospheric magnetic field before being detected on Earth. As a consequence, the observed cosmic-ray arrival direction distribution is affected by the heliosphere as long as their gyro-radius is smaller or comparable with the heliospheric size, i.e. in the TeV energy range. The chaotic nature of those cosmic-ray particle trajectories that are temporarily trapped inside the heliosphere can be characterized using the Finite-Time Lyapunov Exponents. Specifically, we will delve into the case of particles trapped in a heliospheric-inspired toy model of a static magnetic bottle configuration and the presence of temporal magnetic perturbations. In this work, we also suggest that a time-variability could prove to be important in the understanding of the TeV cosmic-ray anisotropy at Earth.