The K [ k ] at the beginning of Lolly’s first time saying this word is not decidedly aspirated, so it would not seem to count as / k / in phonemic terms.  Word-initial voiceless stop consonants in Milluk are generally decidedly aspirated.  Another Milluk word that has an evident sound correspondence involving b-gw is the Milluk word meaning ‘cradle’ which Lolly says in the interview segment "Cradle" on this website.  There too, we find ourselves dealing at the margins with [ k ], where otherwise there is [ g ] and also a sound correspondence with [ b ].