The Deputy Prime Minister ignored complaints about alleged antisemitic posts made by a peer advising ministers on the definition of Islamophobia.
Baroness Gohir is one of five people who were appointed to define anti-Muslim hatred in February.
Ms Gohir had previously claimed Israel "controls" the US in a number of posts on social media, according to The Telegraph.
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Campaign Against Anti-Semitism (CAA) wrote to Angela Rayner in February to alert her to the comments made by Ms Gohir.
Ms Rayner's department is in control of drawing up the Islamophobia definition.
The group referenced five tweets written from 2013 and 2014. It is understood they were public until at least 2022.
However, despite the tweets having been deleted, the group claims it met the IHRA definition of anti-Semitism.
Deputy Prime Minister Angela Rayner
| PAAs the US was considering whether it would take military action against then-Syrian President Bashar al-Assad back in September 2013, Ms Gohir said: "Will Israel influence the US vote on whether to invade Syria?"
"Are the Americans really on control of their own decisions? #JustAsking," the tweet continued.
She tweeted a week later: "Who controls America's foreign policy? ISRAEL - they would be the ONLY beneficiaries of a US attack on Syria."
A year later, she shared a news article which referenced former US President Barack Obama warning Benjamin Netanyahu over him not agreeing a peace deal with Gaza.
Baroness Shaista Gohir OBE | GETTYMs Gohir wrote: "Us warns Israel over Palestine talks failure".
"I bet Israel are quaking in their boots - NOT! Don't they control US?" she added.
Ms Gohir further tweeted in 2014 that "the hold Israel has over world leaders including Muslim ones is extraordinary that they continue to murder Palestinians and get away with it."
The CCA's Director of Investigations, Stephen Silverman, told the Deputy Prime Minister that "according to International (IHRA) definition of anti-Semitism, which has been adopted by the British Government, 'Making demonising allegations about Jews as such or the power of Jews as collective, such as the myth about a world Jewish conspiracy or of Jews controlling the government,' is an example of anti-Semitism".
Mr Silverman added that it was "indeed ... among the oldest anti-Semitic tropes".
He added that "not only is someone who engages in this sort of rhetoric eminently unsuitable for a role advising the Government, but it is particularly ironic that someone who breaches one definition adopted by the Government should be charged with drafting another".
He said that the Government ignoring "its own definition of anti-Jewish racism in the process of crafting and adopting a definition of anti-Muslim hatred" damaged its credibility for both matters.
According to The Telegraph, the CCA followed up with Ms Rayner's team on August 7.
After GB News contacted Ms Rayner for comment a Ministry of Housing, Communities and Local Government spokeswoman said "as set out in the Terms of Reference for the Working Group, all members are expected to uphold the Principles of Public Life".
The spokeswoman added that "The department will shortly be responding to the letter from the Campaign Against Antisemitism".
Speaking to The Telegraph, Ms Gohir said she had deleted the posts "after it became clear that bad actors were deliberately twisting their meaning".
She said her criticism "clearly directed" towards the Israeli Government and not Jewish people.
"That is not anti-Semitism," Ms Gohir said.