I am given a key exchange protocol between a component $C$ and a key master $K$. During the overall execution 4 messages are transferred between $C$ and $K$. DH keypairs are always chosen randomly for each execution.
Message (1) just contains the ID of the component. Message (2) contains the public-key of $K$ and a signature over the key that can be verified by $C$.
This message (2) can be easily replayed by an adversary. On the other hand a replay of (2) will be visible for $C$ after receiving message (4) from $K$ since message (4) contains a MAC whose key is derived from the freshly chosen private part of the DH-key pair (whose public part is contained in (2)).
I am asking myself whether it is a problem from the cryptographic / security point of view that (2) has not freshness protection but any replay will be noticed by $C$ at the end of the protocol execution.