Recently, in [18], a statistical hypothesis test for Long Range Dependence (LRD) in manifold–supported functional time series has been formulated, in the spectral domain, for fully observed functional data. The asymptotic Gaussian distribution of the proposed test statistic, based on the weighted periodogram operator, under the null hypothesis, and the consistency of the test have been derived. In this paper, under a stochastic spatial manifold sampling design, we analyze the asymptotic properties of this statistical test when discretized and irregularly–distributed, as well as contaminated versions of the functional values of the correlated data are available.