I'm not sure how mouch of a settled issue this is. I am way too busy lately, and don't have much time to post. So let me appease my guilt a l ittle.
Thermocouples need to be periodically calibrated (verified, as you can't adjust them) where they are used to measure with any needed accuracy. Where they are installed in systems such as oven chambers, you may verify them by comparison while they are still connected to the oven. If they are removable, you can verify them in a lab.
Using the initial certificate for the roll of TC wire may be okay to fulfill documentation requirements on new TC's, but the final thermocouples need to be verified periodically (again, if you care about the accuracy). I have calibrated thermocouples for many years (particularly those used in high temperature environments, and they absolutely do drift over time. A base metal TC used in relatively low temperatures will not drift very much, but higher temp applications change metal composition through a baking process. Also, buildup of corrosion in the connector can cause additional error, and so must be accounted for as well.
No, you can't adjust them, but you can periodically certify that their output emf is still withing specified limits. And in some circumstances (which I occasionally have to do), you can supply the user with a correction table as appropriate for their use.
Again, this applies linearly to higher temp usage. A type K TC used to periodically check 100 Deg C (for example) may see very little drift over many years. A type R used at 1200 Deg C almost continuously will likely drift 1 or 2 percent within a year or two (depending on particulars of use).