One observation. If someone who has made invalid claims, including via a third party service when they have not actually made the journeys claimed, and they wish to settle, I would suggest wording your email carefully. Say something like "I am not certain these claims were valid and would like the opportunity to repay them" or simply "I would like to settle this matter by repaying the claim". Obviously any offer to pay does not look good, but my point is that saying for example that you relied on a third party service and did not make the journeys is effectively admitting to fraud and makes a prosecution easy. Do not state expressly that you did not make the journeys in question.
In reality GA want to balance (1) resolving these quickly and profitably by settlements, including material admin fees as well as repayment of amounts claimed i expect, and (2) pursuing some via fraud prosecutions for the publicity.
To avoid falling into (2) you need to convey message that you will settle but without clearly admitting you did commit fraud and can be successfully and simply convicted.
To get the message right, and if a fraud conviction would cause you big problems, may well want to use a solicitor.
In reality GA want to balance (1) resolving these quickly and profitably by settlements, including material admin fees as well as repayment of amounts claimed i expect, and (2) pursuing some via fraud prosecutions for the publicity.
To avoid falling into (2) you need to convey message that you will settle but without clearly admitting you did commit fraud and can be successfully and simply convicted.
To get the message right, and if a fraud conviction would cause you big problems, may well want to use a solicitor.