CheckDB won't tell you the last time an index was rebuilt (however you need to run it regularly).
That information isn't stored by default. If you're running a reindexing job, you can look at the job history and see when it last ran. Many custom index rebuild scripts have their own logging table.
Gail Shaw
Microsoft Certified Master: SQL Server, MVP, M.Sc (Comp Sci)
SQL In The Wild: Discussions on DB performance with occasional diversions into recoverability