The police officers who were called to the incident decided to donate £200 to the family from the force's Tuck Shop.
Sergeant Richard Markham, from West Midlands Police, which are investigating the burglary, said:
"Stealing children's Christmas presents is such a heartless and callous thing for anyone to do. We wanted to try and put a smile back on their faces for Christmas.
"We're determined to track down whoever did this and would urge anyone with information that could help to come forward.
"If you know who is responsible please do the decent thing and call us before those responsible cause heartache like this for another family."
More top news
Claire from Leicestershire has raised thousands for charity and her fundraising efforts have now been recognised by the Queen.
West Mercia Police published a statement about its handling of the issue after Sgt Evans requested to keep police dog Ivy after retirement.
Cheryl Stollery from Nottinghamshire said she did not see police "for hours" after the gunman opened fire.