We use time-resolved x-ray resonant magnetic scattering (tr-XRMS) at the Co M$_{2,3}$- and Tb O$_1$-edges to study ultrafast demagnetization in an amorphous Co$_{88}$Tb$_{12}$ alloy with stripe domains. Combining the femtosecond temporal with nanometer spatial resolution of our experiment, we demonstrate that the equilibrium spin texture of the thin film remains unaltered by the optical pump-pulse on ultrashort timescales ($<$1 ps). However, after $simeq$ 4 ps, we observe the onset of a significant domain wall broadening, which we attribute to a reduction of the uniaxial magnetic anisotropy of the system, due to energy transfer to the lattice. Static temperature dependent magnetometry measurements combined with analytical modeling of the magnetic structure of the thin film corroborate this interpretation.