The deuteron tensor analysing power t_{20} of the d(pol) p --> 3He eta reaction has been measured at the COSY-ANKE facility in small steps in excess energy Q up to Q = 11 MeV. Despite the square of the production amplitude varying by over a factor of five through this range, t_{20} shows little or no energy dependence. This is evidence that the final state interaction causing the energy variation is not influenced by the spin configuration in the entrance channel. The weak angular dependence observed for t_{20} provides useful insight into the amplitude structure near threshold.