Benita Mehra said she recognised and respected the "depth of feeling" among some about her appointment.
Downing Street said it had accepted her resignation but maintained there was no conflict of interest.
It comes ahead of the second phase of the inquiry beginning on Monday.
Prime Minister Boris Johnson thanked Ms Mehra for her commitment and said he was "grateful for her sensitivity to the work of the inquiry".
Victims' families had raised concerns to the prime minister about a potential conflict of interest involving Ms Mehra.
They had been threatening to boycott the opening of the second phase of the Grenfell inquiry, which is scheduled to start on Monday.
It has been disclosed that Ms Mehra is a past president of the Women's Engineering Society which, according to the society's website, last year received funding from the Arconic Foundation for an apprentice conference.
Arconic supplied the cladding on the outside of the west London tower block, which caught fire on 14 June 2017, claiming 72 lives.
It was announced shortly before Christmas that the engineer would replace academic Prof Nabeel Hamdi as an expert panellist for the second phase of the inquiry.
The inquiry will switch from focusing on the night of the fire to the refurbishment of the building and its role in the blaze, as well as issues surrounding building regulations.
A report - following the first phase of the public inquiry into the fire - found in October last year that the tower block's cladding did not comply with building regulations and was the "principal" reason for the fire's rapid and "profoundly shocking" spread.
Arconic said a "confluence of unfortunate circumstances" rather than the "mere presence" of the panels had caused the spread of the fire.
It added that the grant was made by its charitable arm, the Arconic Foundation, which is "an independently endowed and managed foundation".