Acquired remote sensing images can be noisy. This fact has to be taken into account in their lossy compression and classification. In particular, a specific noise filtering effect is usually observed due to lossy compression and this can be positive for classification. Classification can be also influenced by methodology of classifier learning. In this paper, we consider peculiarities of lossy compression of three-channel noisy images by better portable graphics (BPG) encoder and their further classification. It is demonstrated that improvement of data classification accuracy is not observed if a given image is compressed in the neighborhood of optimal operation point (OOP) and the classifier training is performed for the noisy image. Performance of neural network based classifier is studied. As demonstrated, its training for compressed remote sensing data is able to provide certain benefits compared to training for noisy (uncompressed) data. Examples for Sentinel data used in simulations are offered.