In MQ, this is usually done with correlation schemes. If you've matched your correlation scheme with what the "real" provider does, your GET should get only the response to that PUT, because it's looking for the same ID.
If your MQ is in JMS mode, there is an additional facility called JMS Message Selector, which allows a GET to inspect a JMS header property for a value, and only consume the message if it matches. JMS Message Selectors are configured in your config assets in DevTest.