  We calculate the finite-temperature Tan's contact for N SU(2) fermions,
characterized by repulsive contact interaction, trapped in a 1D harmonic
confinement within a local density approximation on top of a thermodynamic
Bethe Ansatz. The Tan's contact for such a system, as in the homogeneous case,
displays a minimum at a very low temperature. By means of an exact canonical
ensemble calculation for two fermions, we provide an explicit formula for the
contact at very low temperatures that reveals that the minimum is due to the
mixing of states with different exchange symmetries. In the unitary regime,
this symmetry blending corresponds to a maximal entanglement entropy.
