The Ultimate Airsoft Limited said it had received “hundreds” of requests from customers to shoot at the 19-year-old mum, who is currently in a refugee camp in Syria.
The shooting range, based in Wallasey, said it was “allowing people to have some light-hearted fun, bringing out the inner child in all”.
But some have slammed the firm, with one responding: “Remember, she hasn’t killed anyone.”
The teenager, who fled London aged 15 to join ISIS’s self-proclaimed caliphate in Syria, has said she wants to return to the UK with her newborn son.
Ms Begum, who has had her British citizenship revoked, was one of three schoolgirls to leave Bethnal Green to join the terror cult in 2015 and resurfaced heavily pregnant at a Syrian refugee camp earlier this month.
Pictures emerging from the shooting range show a picture of Begum with around 100 shots in her face.
They are accompanied with the hashtags “target” and “no remorse”.
The firm also uses the likes of Donald Trump, Margaret Thatcher and even Justin Bieber as targets.
An investigation by the BBC found kids as young as six visit the range.
Speaking to The Sunday Telegraph from the al-Hol camp in Syria, Ms Begum said: “They are making an example of me. I regret speaking to the media. I wish I had stayed low and found a different way to contact my family. That’s why I spoke to the newspaper.”
The Home Secretary revoked Ms Begum’s British citizenship in a move only permissible under international law if it does not leave the individual stateless.
It was speculated that Ms Begum, who is of Bangladeshi heritage, may have citizenship there but Bangladesh’s minister of state for foreign affairs Shahriar Alam denied this.
Her family have written to the Home Secretary asking for his help to bring her newborn son to Britain.
The letter to Sajid Javid said the baby boy was a “true innocent” who should not “lose the privilege of being raised in the safety of this country”.
Her sister Remu Begum, writing on behalf of the family, asked how they could help the Home Secretary “in bringing my nephew home to us”.
The family said they have had no contact with Ms Begum and had only learned she had given birth to a boy through media reports.
“Remember, she hasn’t killed anyone”
They made clear that they were “shocked and appalled” at the “vile comments” Ms Begum had recently made to the media.
Mr Javid’s removal of her citizenship came amid heated debate over whether the teenager should be able to return to the UK after she was found in a Syrian refugee camp with the terror group’s reign nearly over.
While many do not want to see Ms Begum return to the UK, others have argued she should face prosecution for her actions, and attempts at deradicalisation.
The Begum family’s lawyer Tasnime Akunjee said she was born in the UK, has never had a Bangladeshi passport and is not a dual citizen, which was confirmed by the Bangladeshi minister.