My question is about “getting it”. Does it mean to thank sb. for his attaining sth.? Or, does it mean to thank sb. for settling sth.？Or, to thank sb. for understanding eth.?
Getting it is basically get, with a noun (it or other things). Get can mean receive, acquire, understand, etc.
Check this link for the definition of the word get:
So, thank you for getting it could mean thank you for understanding, et cetera., depending on the context.