Hundreds of blue bows have been placed at the scene in Brownhills High Street and around the local area after baby Ciaran Leigh Morris's pram was hit by a car on Easter Sunday.
Video footage was then posted on Facebook showing someone removing one of the bows after getting out of a 247 Cars taxi.
Hundreds of people have since shared the video online.
The company later responded with an "official statement" saying the driver had been suspended while an investigation takes place and that the company would be donating to the fundraiser set up for Ciaran's family.
Screenshots posted online show messages appearing to have been sent from the firm's head of customer relations saying the driver was travelling with his pregnant wife who stopped to get fresh air, and that the bow fell after she touched it.
A spokesman for the company has since said: "We have concluded looking into the matter and the driver no longer works with us."
The community in Brownhills has rallied behind Ciaran's young family after the baby boy's death.
As well as the blue bows, dozens of tributes were left at the scene of the crash, fundraising events and auctions have been organised and a JustGiving page set up to support the family has now raised more than £34,000.
Ciaran was being pushed along Brownhills High Street on Easter Sunday when a BMW hit the pram and pinned it against a wall, after colliding with a Ford C-Max.
A 34-year-old man alleged to have been driving the BMW has been charged with causing Ciaran's death and appeared in Wolverhampton Magistrates Court on April 6.
James Paul Davis, of Croxtalls Avenue, Walsall, is charged with causing death by dangerous driving, causing death by driving while uninsured, leaving the scene of a collision and failing to report a collision. He will next appear at Wolverhampton Crown Court on May 4.
247 Cars' earlier Facebook post said: "This is an official statement from 247 Cars with regards to an incident that occurred on Thursday 8th April 2021 in Brownhills.
"A video footage has emerged of a car with 247 Cars branding taking part in what appears to be the removal of a bow from a memorial for Ciaran Leigh Morris who tragically lost his life in a road traffic collision on Easter Sunday.
"We regret the incident and our team immediately started looking into the matter.
"247 Cars is a highly respected regional company operating in 13 town and cities of the West Midlands. With over 700 drivers, we had to be aware of all the facts and identify the individual involved in this unfortunate incident.
"247 Cars operates according to three timeless principles known as Core Values, our response is therefore guided as follows:
"We Get the Job Done: We have suspended the self-employed driver from working on our data circuit pending a full inquiry.
"We Care About Getting it Right: We believe in doing the right thing and although all comments have been read, we regret we cannot reply to every post individually.
"We were first made aware of this matter by Facebook private messenger at 8pm on 8th April.
"As per our customer service policy, we are officially responding to the complaint within 3 working days.
"We Lead, Others Follow: Although the driver is not an employee of 247 Cars and the actual act of removing the bow was committed by a paying passenger, we do take responsibility for responding to misdemeanours committed by drivers or passengers whilst using our brand and reputation.
"We wish to apologise unreservedly for the added anguish caused to all concerned during this, already difficult time.
"247 Cars will be making a donation to the fund set up to support the family of Ciaran.
"We always will lead from the front and do what we can in the form of restitution when things go wrong. We have and will take all the possible steps to make things right."