  Nematic order in the iron-based superconductors is closely tied to a lattice
distortion and a structural transition from tetragonal to orthorhombic
symmetry. External stress of the appropriate symmetry acts as a conjugate field
of the nematic order parameter and can be utilized to detwin nematic domains
but also smears an otherwise sharp nematic transition. On the other hand,
applying stress in proper symmetry channels allows one to tune the nematic
phase transition. Recent experiments analyzed the stress-induced changes of the
nematic and magnetic phase transition temperature. Here we show that the
observed trends can be understood in terms of spin-induced nematicity. The
strain sensitivity is shown to be a fluctuation effect. The strong sensitivity
to antisymmetric strain is a consequence of the anisotropic nature of the
magnetic excitation spectrum. The formalism presented here can be naturally
generalized to determine the strain-sensitivity of vestigial phases related to
other magnetic states that have been observed in the iron-based systems, such
as e.g.\ the spin-charge density wave and the spin-vortex crystals.
