Unfortunately, the only information I have was provided in my earlier response. I believe Mr. Squires came to the Grand Lake area from St. John's and was involved with the Newfoundland Railway or Telegraph Company. Bertha Oliver was a domestic in the Bay of Islands area. They would likely have met when Squires came there for supplies or work related reasons.
I have a vague memory of someone referencing that Bertha lost her parents in a fire somewhere around Rigolet, but that may have just been based on hearsay. The surname Oliver would indicate that she was likely of European descent as well as Inuit. You could research the HBC records (reposed in Manitoba) for the original Oliver who was likely a Scotsman who came out with the HBC. I believe a man named Oliver also assisted Mina Hubbard on her Labrador journey. There may be some glimpses in Them Days, a publication in HV-GB. Your best bet is to get in contact with someone form the family. There must have been an historian there somewhere. Try the Elms in St. Anthony or the Banfields in Stephenville.
If you find something out, please share on here.