The main conclusion of this study is that the degree of alteration of the fossils, derived from IR spectral analysis, seems to be well correlated with the sample age, and that terrestrial fossils after a billion years are so altered that it becomes impossible to trace their biotic origin. Since it is reasonable to assume that the putative Martian fossils should be at least 3.5 billion years old, this would imply that our spectroscopic method could not be able to detect them, if their degradation rate were the same as that we have found in usual conditions for the terrestrial fossils. However, due to the different climate evolution of the two planets, there is the possibility of having two different degradation rates, much lower for Mars than for Earth, especially if the fossils are embedded in a protective layer, such as a clay deposit. In this case IR spectroscopy, coupled with thermal processing, can be a useful tool for discriminating between abiotic and biotic (fossil) carbonate samples collected on the Martian surface.