Can you specifiy which GTP-TEID you mean here ? GTP-C TEID or GTP-U TEID ?
If you asked for GTP-U TEID, then there has to be a one to one mapping between a GTP-U TEID and the EPS bearer at different end points like eNodeB, S-GW and PDN-GW, across their supported interfaces on the data flow path.
If it is a GTP-C TEID, then it is interpreted differently across different interfaces
1. On S11, there has to be only one pair of GTP-C TEID (one on MME and the other on S-GW) for one UE. This must be shared for all the control messages' related operations related to this UE.
2. On S5/S8, the GTP-C TEID has to be unique per PDN connection. And this has to be shared among all the EPS bearers which use this PDN connection. (However the spec doesn't mention anything about the UE here).
Some more interfaces like S3, S10, S16 which are dependent on LTE, See spec 29.274 section 4.1