Fly swarms from the Shows Waste Management site in Slack Lane, Derby, have left residents facing difficulties cooking and cleaning for weeks.
Shows has removed 3,018 tonnes of waste but because of "weather and transport", about "700 to 1,000" tonnes remain.
The agency has begun an investigation into the cause of the swarms.
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About 3,000 households and businesses are in the affected areas, prompting Shows to be suspended on 17 May from taking waste.
Resident Amanda Cairns has called for compensation for people affected, but the agency said this was a civil matter.
Ms Carins said: "You couldn't cook. If you put your cup down on the table, you got flies landing in your cup of tea or coffee."
"You were sterilising your worktops non-stop. We had to have nets upon doors, fly sprays, I've tried vodka, basil, everything."
Another resident, Melissa Marriott, previously told the BBC she had been unable to have a bath without flies getting into the water, and had to resort to buying an electric fly killer which "gets 50 flies a day".
In a statement, a firm spokeswoman said: "[Shows] can confirm 3,018 tonnes of waste has been removed. However, due to unforeseen circumstances with weather and transport a small residue remains.
"We can also confirm the fly situation has now been resolved with no reported issues since early June.
"[Shows] would like to assure all residents and the agency all endeavours are being made to clear the site completely."
It said it had become involved in the current situation because of a dispute with another firm.
The Environment Agency said an estimate of "700 to 1,000 tonnes" of waste is still awaiting removal, but last month it said the fly issue had been resolved.
"We appreciate that we set a tight deadline and at times during the process we believed it would be met," a spokesman said.
"Moving this amount of waste was always going to be a huge logistical exercise for the operators and significant progress has been made."
A recycling firm has failed to remove waste that caused homes to become filled with flies to hit an Environment Agency deadline.