Royalty-free images give you nearly unlimited use. You are allowed to use the image in many different projects as you like. Having said this, your limiting factors will be clearly listed in the terms and conditions of Thinkstock. I suggest you go back and carefully read through the service terms and agreement.
You're using these images in multiple client projects, for which the clients are compensating you. I would suggest you look for such limiting language within Thinkstock's terms and conditions. A possible argument is that this constitutes resale of the images you are purchasing from them.
In summary, your rightful use of the images will be heavily dependent on the terms of the agreement. You will have to go and study them and see if the limitations in those terms fit your scenario.
Your particular situation may be different. This answer is intended for information purposes only. No Attorney-Client relationship has been established.