We often get that kind of question, so have a look at the kind of data we have to work with.
Mountain chains are highly dynamic environments which form in collision zones between 2 plates. Rocks from different initial depths are rearranged and [thrust/folded into different configurations](ftp://184.108.40.206/pub/avouac/Ge277-2010/Davis1983.pdf
). At some point the process stops and you reach "peak mountain building" ... The mountain chain is at its tallest, and it all downhill from there (sorry). If you had a time machine you could actually go and measure the maximum altitude reached. But we can't and we don't.
By the time we get to looking into those matters, time has passed and erosion taken large parts of the mountain chain away. So, what we actually do is look at the chemistry of the minerals which make up the metamorphic rocks formed under that mountain chain. As rocks of a given composition are brought to different pressure (P) and temperature (T) conditions, they undergo chemical reactions and re-equilibrate to different mineral assemblages. Some of these assemblages are particularly sensitive to temperature and pressure and act as [geothermobarometers](https://en.wikipedia.org/wiki/Geothermobarometry
). They may rely on the ratios of trace elements incorporated in a specific mineral, or on isotopic ratios. Garnets and amphiboles are particularly well suited for these kind of studies, and allow the calculation of [P-T paths](https://www.researchgate.net/profile/Jane_Selverstone/publication/220021207_P-T_paths_from_garnet_zoning_A_new_technique_for_deciphering_tectonic_processes_in_crystalline_terranes/links/5489e1140cf214269f1abe5b/P-T-paths-from-garnet-zoning-A-new-technique-for-deciphering-tectonic-processes-in-crystalline-terranes.pdf
), a historical trajectory through Temperature-Pressure space through which a given rock has passed. Add to that the possibility of using amphiboles or other minerals as geochonometers and you can calibrate those paths into the time (t) dimension, generating a P-T-t path. This allows you then to determine how much pressure that rock was under at a given time. But (and it's a huge but), translating that data into mountain altitude is not an easy thing. You have to make assumptions about heat flow, because geothermobarometers are temperature-dependant. There is a marging of error on the initial measurements, and they add up. So in the end you wind up with a range of possible heights, which seldom satisfies whomever asked the initial question.
I hope this clears things up.