Ms Jones, deputy chair of the police and crime committee, suggests the money saved by scrapping the TSG should be spent on better police riot training.
The unit's commander said it was working to engage young people.
Chief Supt Mark Bird said Ms Jones's recommendation to the mayor would leave London without a round-the-clock response to critical incidents such as murders.
In Ms Jones' report, The Kids are All Right: How the Metropolitan Police can gain the trust of young Londoners, she recommends ways to improve confidence in the force.
'Think they are special`
She writes: "The Met should scrap the TSG and use that funding to train a greater number of police officers for public order situations.
"If the mayor is unwilling to call for this he should prioritise youth training for TSG officers."
About the TSG
- Created in 1987 to replace the Special Patrol Group
- A high level of fitness is required
- Applicants must be recommended by a senior officer
- The unit claims it can fully train and deploy officers in any new skill within five weeks
- The TSG can respond to chemical, biological, radioactive and nuclear incidents
She also suggests more school visits and youth training for officers.
The TSG, set up 25 years ago, is tasked with tackling terrorism, providing an immediate response to disorder and reducing priority crime.
Speaking to BBC London, Ms Jones said: "They think they are incredibly special.
"That generates a feeling that they can do things differently from other police officers.
"If you see police acting like some sort of paramilitary body I think it is bad for the police."
Janette Collins who runs The Crib, a youth project in Hackney, said: "The reason why young people don't trust the TSG is that there's so much different policing in London they don't understand the policing.
"When they call the TSG out to come and deal with an incident in an area they just come along, rush in, rough everybody up and then [they are] out the area again.
"That leaves the safer neighbourhood team to have to pick up the pieces, which is unfair."
The TSG said youth engagement activities had been increased to tackle "perception" problemsTSG commander Mr Bird said the unit had a "perception problem".
"It is this notion that we do the work and move out when in reality the TSG is spread across 32 boroughs.
"Twelve percent of our time is spent dealing with disorder and riots, the rest is in supporting the boroughs."
He said a community reference group was set up last year to look at perception, recruitment, selection and complaints.
He said between 2008 and 2012 there had been a 50% decrease in the number of complaints made against the TSG.
I do not mistrust them, mostly because I have not broken the laws they enforce. I get thou the funny feeling this bunch calling for the scrapping of a Police department, would like to see the whole Force disbanded.
"'Think they are special`" They sort of are.
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