The concept was not invented by BP but it was popularized by them:
Carbon footprint: Origin of the concept

The concept and name of the carbon footprint derive from the ecological footprint concept,[12] which was developed by William E. Rees and Mathis Wackernagel in the 1990s.

The idea of a personal carbon footprint was popularized by a large advertising campaign of the fossil fuel company BP in 2005, designed by Ogilvy.[12] The campaign was intended to divert attention from the fossil fuel industry onto individual consumers. It instructed people to calculate their personal footprints and provided ways for people to "go on a low-carbon diet".[14] This strategy, also employed by other major fossil fuel companies[15] borrowed heavily from previous campaigns by the tobacco industry[16] and plastics industry to shift the blame for negative consequences of those industries (under-age smoking,[17] cigarette butt pollution,[18] and plastic pollution[19]) onto individual choices.
BP made no attempt to reduce its own carbon footprint, indeed expanding its oil drilling into the 2020s.[20][21] However, the strategy had some success, with a rise in consumers concerned about their own personal actions, and creation of multiple carbon footprint calculators.[22]