Nabil Choucair, who stood watching the tower burn on the early hours of 14 June last year, met with the Prime Minister in Westminster along with more than a dozen other families.
They have been campaigning for the establishment of a diverse panel with decision-making powers to be set up as part of the inquiry.
The meeting came ahead of a debate in Parliament next week discussing a petition, backed by rap artist Stormzy, asking the Prime Minister to improve public trust into the inquiry.
Mr Choucair described Thursday’s meeting as “a total let down” and told Sky News he is “really upset and disgusted with how she has handled it and dealt with it”.
He said Mrs May responded to their request and petition by saying she would “reflect on it”.
The tower fire in west London killed 71 people.
Following the meeting, Mrs May was presented with a print of a painting by Damel Carayol, adorned with the caption: “Eyesore!! Final Straw.”
The 55-year-old artist, from north London, lost family members in the fire. One of them was his niece Khadija Saye, a fellow artist who died shortly before her work was to be exhibited for the first time.
After hearing reports a few days after the fire that the fatal cladding was attached to the building for aesthetic reasons, he told Sky News “that tipped me over the edge… it was pure anger. I didn’t plan or think I just grabbed my one canvas that was left”.
“My anger just poured out through the paint… it was pure anger and sweat and swearing and everything,” he added.
A message written on the painting reads: “To the Prime Minister Mrs Theresa May. Given from a good place with a righteous message. We all hope and pray that nothing like this will ever happen again.”
Mr Carayol says he presented it as a gift to Mrs May, who called it “powerful”.
Mr Choucair, who lost his mother, sister, brother-in-law and their three children, told Mrs May he has no confidence in her.
He says he feels like Mrs May was not listening to the points raised by the group, saying: “It’s like we’re talking and it’s going in but then out the other ear.”
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“It feels really very painful, very hard and having to go through it and keep going through it – it’s enough that we are all suffering… but we have to go and ask for this panel which she should clearly have understood from the first place… she’s caused a lot of pain and more suffering unnecessarily.”
Downing Street has declined to comment on the matter to Sky News.