If anyone asked me to use such a framework, I would give the lead some serious second thoughts.
If the customer has the time to micromanage me or look through such footage, they have focused on the wrong things (huge red flag project-wise). I have experience with this as an employee (call center environment) and it never ends well.
What is ostensibly intended to provide for good things inevitably leads to bad including possible disclosure of sensitive information (checking your bank account after forgetting to log out), or giving a belligerent customer things they can rip out of context to try to say they shouldn't pay.
Really, if you have any other choice do not do this.
If you do this, you have to figure that any activity on your computer at any time could be accidently disclosed to your customer. This could include without limitation trade secrets of other customers, confidential information you have agreed to protect, your own financial information (including but not limited to credit card information sufficient to make purchases online), and much, much more.
Note additionally my experience was in the formal employment context. Those risks go up quite a bit for consultants and contractors since typically you own your own computer and use it for other things too.
This being said, very often it is very helpful to give customers a detailed breakdown of what you did for them, how long. LedgerSMB (disclaimer: I run a LedgerSMB hosting service with a business partner too, as well as do development and consulting on that platform) has a timecard interface where you can assign timecards with projects, add detailed notes, and include those notes, optionally on invoices you send your customer. It is fairly simple: you enter a time in and time out, it calculates an interval at the rate associated with the service and customer. You indicate how many of those hours were non-billable and give both description and notes.
Then you can generate sales orders from a set of timecards, and sales invoices from the orders.
I would hope that many other applications have similar functionality.
If you absolutely must
From my perspective the only reasonably safe way to address this is to create a screencast of your work, and at least check the ends (make sure you didn't leave it running when you were done and went to check, for example, your bank account).
Specific recommendations for software to accomplish this is probably outside the scope of Q&A because such a list will likely go out of date relatively quickly but Wikipedia does maintain a list of such software which may be of help.
A final alternative might be to require that a customer with such a requirement provides you a computer for sole use for you to use in working on their project configured to their specifications. This way you have an air gap between anything your business might consider sensitive and anything the customer gets to see.
However this is a business security nightmare. If you have any confidential information on your computer at all, it is not safe, and if you inadvertently violate another client's NDA, you might be held liable.
Finally, if you absolutely must do this, please discuss the relative impact of accidental disclosure of any NDAs currently in effect with a licensed attorney.