It's probably worth pointing out that this isn't a Single Justice Procedure Notice: it's what we tend to call a 'verification letter' from TfL. So you haven't yet been charged with anything - and while you're not obliged to get involved in the process, in practice it's probably a good idea to take the chance to try to head off a prosecution before it begins.
So as
@Snow1964 suggests above, think about whether you used TfL services at all last Friday. Check the bank/credit card statement for your contactless to see if they give any help. And if it turns out that you didn't travel anywhere with TfL on Friday, then write back to tell them so.
It might also be worth thinking hard about whether you ever had a registered Oyster card: if it turns out that you did, do you know where it is? Might someone have 'borrowed' it without your knowing? I can see that as a possible way which might have started this hare running.
Bearing in mind the following
Think hard about whether 'forgetting to tap' may amount to an offence: it seems to me that if you remembered to tap at one end of a journey you will face a maximum fare because the system will work out a fare for you. If on the other hand you forgot to tap at both ends that could be rather more serious.