Classification of remote sensing multichannel images is a typical operation where several factors can influence its efficiency. In this paper, we consider three factors, namely the influence of the residual noise after lossy compression applied to original images supposed noisy, the impact of data used for neural network training with further application of classification to lossy compressed image, and an opportunity to partly improve quality of compressed images by their post-filtering after decompression. We demonstrate that 1) the classifier training for conditions (compressed image quality) for which the classifier will be later applied improves classification performance; 3) post-filtering can improve classification if properly applied and efficient. The experiments are carried out for two real-life three-channel Sentinel data of different complexity to which additive white Gaussian noise has been artificially added.