OK, found the answer myself. The API I used is deprecated, but it worked when running against RTC3.
The code snippet below provides the means to check if a given work item has a "copies" link; and if so, that is removed. Note: RTC is really cool here - removing all the "copies" links ... will also result in all your "copied from" links being gone afterwards.

    void fix(IWorkItem workItem) throws TeamRepositoryException {
        IWorkItemWorkingCopyManager mgr = workItemClient.createWorkingCopyManager(userName, true);
        try {
           mgr.connect(workItem, IWorkItem.FULL_PROFILE, monitor);
           WorkItemWorkingCopy workingCopy = mgr.getWorkingCopy(workItem);
           removeCopiesReference(workingCopy);
           mgr.save(new WorkItemWorkingCopy[] { workingCopy }, monitor);
        } finally {
            mgr.disconnect(workItem);
        }
    }

    void removeCopiesReference(WorkItemWorkingCopy workItem) throws TeamRepositoryException {
        IWorkItemReferences allReferences = workItem.getReferences();
        List<IEndPointDescriptor> endPointTypes = allReferences.getTypes();
        for (IEndPointDescriptor endpoint : endPointTypes) {
            List<IReference> references = allReferences.getReferences(endpoint);
            for (IReference finalRef : references) {
                IWorkItemHandle h = (IWorkItemHandle) finalRef.resolve();
                if (h == null) continue;
                IWorkItem w = workItemClient.resolveWorkItem(h, IWorkItem.FULL_PROFILE, monitor);
                if (endpoint.getDisplayName().equals("Copies")) {
                    monitor.subTask("Removing 'copies' link from ID: " + workItem.getWorkItem().getId() + " (target was): " + w.getId());
                    allReferences.remove(finalRef);
                }
            }
        }
    }