  In superfluid $^3$He-B confined in a slab geometry, domain walls between
regions of different order parameter orientation are predicted to be
energetically stable. Formation of the spatially-modulated superfluid stripe
phase has been proposed. We confined $^3$He in a 1.1 $\mu$m high microfluidic
cavity and cooled it into the B phase at low pressure, where the stripe phase
is predicted. We measured the surface-induced order parameter distortion with
NMR, sensitive to the formation of domains. The results rule out the stripe
phase, but are consistent with 2D modulated superfluid order.
