No, it is not unreasonable. The company is investigating potential fraud, and so you shouldn't be surprised to ask to account for your actions if they are under suspicion. If the file was passed to the police, you could expect to be arrested (subject to the strength of the evidence GA has) and interviewed, and asked exactly the same thing.
If you do not have evidence of your journeys, then I don't think that's especially surprising, so, assuming you have never fraudulently claimed Delay Repay, write a brief letter back to them and explain something along the lines:
Thank you for your letter of (X date).
I do not keep records of my journeys and, as a paper ticket holder, am sure you understand that I cannot provide you with evidence of journeys made. I have only ever claimed Delay Repay with honest intentions, and can say that every time I have claimed it was in line with the scheme conditions as I understand them.
Kind regards
X
The matter will likely then just go away, unless of course, you've made claims which are dodgy.
Has this ever happened to you? Was it the reason for putting in a claim which may appear to be inflated from GA's perspective?
If I turn up at Euston at 4:45pm for the 5pm train and see all trains are cancelled, and decide to stay in town until 8pm for a few bevvies, it is improper to file a claim for a three hour delay, if trains begin running again at 5:30pm and I could have got back much earlier.
"Do not travel" advice is intended to prevent people from travelling, but the railway knows some people will always want to catch the train. If I am advised not to travel on Sunday because there is a vastly reduced service, but travel anyway, and incur a delay against the timetable, a claim is perfectly okay.
If you read the whole thread, you can see numerous people paying up because they submitted fraudulent claims, and a couple who seem to have been caught in the net unwittingly.
I suppose the golden question is, did you submit any claims dishonestly? If you did, I recommend engaging with the process to settle to avoid the matter being passed to the police. If you didn't, and your conscience is clean, see my earlier advice, and advise the company quite simply that you have only ever claimed in line with the conditions.