in our outfit the captain reports what he thinks is a hard landing - engineering then checks the data readout to detirmine the actual 'g' value and v/s at touchdown, dependind on these the actions (or lack of) are given in the maintainance manual
if not reported, 1.5g and above throws up a flag during routine dfdr analysis, 1.8 is cause for a chat. mitigating factors such as a well stabilised approach maybe taken taken into account before calling for a chat.
in my experience, anything much over 1.5g can definitely be felt as unusual and should be reported for the good of the next crew.