The report, Plan A+: Creating a Prosperous Post-Brexit UK, published last year, had been removed from the IEA’s website after, in February, the commission deemed its publication and an associated launch event "amounted to misconduct and mismanagement".
This led to the Charity Commission issuing an official warning to the IEA, claiming the report and event were insufficiently balanced.
But in July the commission rescinded the official warning after it decided it had not handled the case sufficiently well.
In a statement published at the time of the warning’s withdrawal, the commission said a review of the decision by a board member at the regulator found the charity had "taken remedial action in relation to the breach".
But that statement also said that the warning was properly and lawfully made, and that the original report breached charity law.
The IEA has now republished the report with alterations.
The appendix to the report highlights some of the changes that have been made, covering the executive summary and chapters three, four, five and six.
The changes include softening language and tone to ensure readers are aware the report’s suggestions are one of a number of options for Brexit.
A spokeswoman for the IEA said the Charity Commission had reviewed the new version of the report and had made a small number of further suggestions for the IEA’s staff and trustees.
A spokeswoman for the Charity Commission said: "We are aware of the publication of the IEA’s revised report.
"The responsibility lies with the trustees to ensure the updated report furthers the charity’s objects and is in line with charity law."