The National Association of Head Teachers urged its members to draw up lists of additional expenditure incurred by the delays, which stopped thousands of pupils attending school at the start of term.
David Hart, NAHT general secretary, said: "Neither the Government nor Capita (which provides services for the Criminal Records Bureau) should be in any doubt about the anger felt in schools."
The move came as former Europe minister Keith Vaz called for a debate on the CRB when Parliament reconvenes.
The Leicester East MP wants compensation for schools and believes that parents should be recompensed for inconvenience caused when children were sent home. "Parents have had to give up work to look after their children," he said.
The CRB is considering claims on a case-by-case basis, but will only pay out for specific proven errors rather than the delays.
Other problems to emerge with the criminal checks this week included a loophole in the vetting of the 8,000 staff who arrive each year from overseas. The Department for Education and Skills admitted that countries such as South Africa, which supply "certificates of good conduct", may not run full checks for criminal convictions.
Several councils have banned parents from schools, except to bring children and speak to teachers. Parent helpers were unhappy about not being allowed to work in schools without checks, which cost pound;12 each.
A team of troubleshooters is due to report to Home Secretary David Blunkett on Monday on the problems at the CRB.
Mr Blunkett wants to see "solutions not scapegoats", but Capita fears it will be blamed after reports that the Home Office is considering ending its pound;400 million contract to provide services to the CRB over 10 years.
Shona Nichols, group marketing director of Capita, said the company regretted the part it had played in the recent disruption to schools.
She added: "We are working hard with our colleagues in the CRB to ensure that service efficiency improves to meet the needs of applicants and employers."
A DFES spokeswoman said a handful of schools had turned away teachers this week after discovering their names were on its List 99 dossier of unsuitable people.