"To investigate the claims" means to carefully examine or look into the statements or allegations that have been made to find out the truth or gather evidence. Full definition
The secretary of state takes on the responsibility for the training of teachers; for investigating claims of misconduct against teachers and the power to ban them from working in schools. (bbc.co.uk)
Insurance companies that deny legitimate claims, delay or make only partial payments or refuse to investigate a claim in a timely fashion are said to be operating in bad faith. (coloradoinjurylaw.com)
I hold the record for reading that book in two weeks... your opinion isn't valid if you didn't thoroughly investigate my claim. (religion.blogs.cnn.com)