No, definitely not! TERMINATION can't be used here, but "permanently laid off" can. I don't think there is a need to explain when and why we use TERMINATION or what conditions apply in this regard, but certainly, we can't use this "Termination."
I second Mr. Ponraj. Is the employment letter containing a condition that you can terminate any employee if required after the completion of the project/work/contract? What does the notice period clause say about it? Do you have any Lay-off Policy?
I agree with your colleagues who are objecting to this word because employees have done nothing wrong that can be the reason for their termination, but you are relieving them with your reasons. You can issue them a "Lay-Off Notice" mentioning the reason that you are going to relieve them but can't terminate them.
I don't think there is any organization that is using this kind of terms and conditions of employment in an employment/appointment letter that any EMPLOYEE CAN BE TERMINATED without any mistakes or being a reason for some disciplinary action or anything like that.
But yes, if you are using this word within your employment policy and under the employment conditions, which is really sad, I would say and must not be used, you can go ahead but need to correct it actually.