If a check for a contribution to an IRA bounces- what happens to the earnings that accrued on the amount while it was in the IRA?

No guidance has been issued for this scenario. However I borrow from [Springfield Productions, Inc, 38 TCM 74 (1979)], where it was determined that " If the check bounces, no contribution is deemed to have been made", ergo, no earnings that accrued from such contribution belongs to the account and should be removed, as soon as administratively feasible, without causing any tax reporting.

The IRA custodian must make the decision of who is entitled to the earnings.