Hrrmm... for "object" based AWS stuff, it's fairly easy: you add a tag[1] to the resource (an EC2 instance for example) and those tags are exposed in the billing reports, so you can correlate them back to your customer accounts. I haven't used any of the "pure api" based Amazon services, so not sure if there's an exact analogue of that or not. I see that there's a jobTag[2] field you can add to the request for Textract calls, and that that can in turn be sent to an SNS topic.
If that same field makes its way into the billing report, this would be fairly easy. If not, I think you might just have to track how many calls are made on behalf of a given customer (your customer) and then write code to calculate how much to charge your customer based on the published pricing information[3] for the service. You could do the tracking using that jobTag thing and SNS topic, or you could probably track it on your end if there is code you control that is actually initiating the Textract request. One tricky part here will be keeping track of price changes and when they happen, so you can reflect that in your calculations.
Maybe there's a cleaner way to do it. Ideally there'd be a way to pass something in the request that flows all the way through to the billing report, but I am not sure if that "thing" exists for these services or not.
[1]: https://docs.aws.amazon.com/awsaccountbilling/latest/aboutv2...
[2]: https://sdk.amazonaws.com/java/api/latest/software/amazon/aw...()
[3]: https://aws.amazon.com/textract/pricing
