IPA: /ˌɪrɪˈkleɪməbli/
KK: /ɪrɪˈkleɪməbli/
In a way that cannot be recovered or reclaimed.
The land was irreclaimably damaged by the oil spill.
Irreclaimably → It is formed from "in-" (meaning not), "reclaim" (from Latin "reclamare", meaning to cry out against or to reclaim), and "-ably" (meaning in a manner that can be). The word means in a manner that cannot be reclaimed or recovered.
Think of 'not' ('in-') being able to 'reclaim' something — that's why 'irreclaimably' means it cannot be recovered.