How are turbine blades overhauled?
Discs, blisks, and blades are all very expensive components so if they can be salvaged through repair and overhaul programs they usually are. According to this article overhauling a high pressure turbine blade from the CFM56-7BE is 80% cheaper than producing a new one, which is roughly inline with my experience. The actual overhaul process will vary depending on why the item was taken out of service and what condition it is in. There are many companies out there that are built around overhauling various components of gas turbines and many OEMs like RR &amp; Siemens have programs or side businesses for it.
Compressor blades
For a compressor blade a full inspection is required to check it still meets the original specification. This would include at a minimum:

Visual inspection for nicks, scratches, or any other damage
CMM inspection (or equivalent) for shape and size
Weight and balance measurements

If there is any damage to blade it may be possible to repair them through welding or other approved methods depending on the location and severity, but I've never actually come across any company doing so for compressor blades, they're normally discarded.
Turbine blades
All of the above also applies to turbine blades, except that they often can be welded and repaired if they're cracked. They're much thicker and sturdier than compressor blades. If the blade is coated, (pretty much all modern blades are) the coating will have to be removed, replaced and re-inspected for thickness. There will also be a check that all the cooling holes are clear and functional.