Don’t recall Inmarsat giving details of altitude of pings, simply distance.
I very much doubt that they can derive altitude, for two reasons.
The aircraft is a minimum of 36,000km from the satellite. So the difference between, say, FL280 and FL410 represents around 0.01% of the satellite-to-aircraft distance, which is very unlikely to be discernible given the tolerance on the ping-derived range.
But even if it was, how do you tell the difference between an aircraft on the X° curve and one slightly farther from the origin but at a higher altitude i.e. exactly the same slant height from the satellite?