Scottish Borders Council will set up a working group to examine how it handled the procedure.
It comes after more than 4,000 people signed a petition against the project, to which the council allocated Â£3.5m.
Concerns have also been raised that its planning application was approved by a committee of just four members.
Tweeddale councillor Keith Cockburn said the group will address "public disquiet" over the decision-making process.
"We can definitely make sure that we can learn some things about the consultation," he said.
"There's been many questions about how we looked at the alternative sites, how we looked at the feasibility of the business plan, etc.
"A decision has been made so we have to recognise and respect that, but also look at what we can learn from it."
A petition against basing the tapestry at Tweedbank was considered "very carefully" by councillors, council leader David Parker said at the time.
However the petitions and deputations committee decided to take no further action.
Councillor Jim Torrance said the working group was not needed as the subject had been fully debated twice at council.
"It's been debated so much I don't see what any working group is going to find out from it that's going to be of any use," he added.
The council's scrutiny committee voted to set up a tapestry working group at its next meeting.

The 23-year-old joined Barrow at the start of the season from Stenhousemuir but made only six National League appearances for the Cumbrian side.
Murray began his career at Scottish club Motherwell and also had spells with Arbroath and Clyde.
Southport are 19th in the table, two points above the relegation zone.

Tariq Hameed Karra described government policy as "brutal" and condemned his People's Democratic Party for its state-level alliance with the BJP.
He quit his party and resigned from parliament.
More than 80 people have been killed since wide-scale riots erupted in early July.
The mass closure of mosques in Kashmir hampered the festival of Eid al-Adha this week.
"For the first time in history, the people of Kashmir were not allowed to offer Eid prayers. Certain shrines and even the Grand Mosque were locked,'' Mr Karra told reporters on Thursday.
"Kashmiri blood is being spilled on the walls, lanes and drains of the valley," he added.
The demonstrations were sparked by the killing of a popular militant leader, Burhan Wani, 22, in a gunfight with the army.
Disputed Kashmir is claimed in its entirety by both India and Pakistan and has been a flashpoint for more than 60 years, causing two wars between the neighbours.
Within the disputed Muslim-majority territory, some militant groups have taken up arms to fight for independence from Indian rule or a merger with Pakistan.
The process which led to the decision to house the Great Tapestry of Scotland in Tweedbank is to be the subject of an investigation.
[NEXT_CONCEPT]
Southport have signed defender Euan Murray from fellow National League club Barrow on a deal until the end of the season.
[NEXT_CONCEPT]
An MP from the ruling party in Indian-administered Kashmir has resigned to protest against the way authorities' have handled weeks of political unrest.