Well if they did, though, wouldn't they spot anything left in his system that could account for his lingering contact with the collective?
I sort of doubt it. At that point, they didn't even appear to know about the Borg nanoprobes (even though an injection made Picard go grey in "BoBW pt I"); they might very well have thought that taking out the macroscopic add-ons would be the end of it.
It's not as if the contact is "lingering" but more like "dormant", only manifesting on certain encounters and not on others. That would jibe well with a subspace transceiver that is built by the nanoprobes as needed and then torn down again.
There could be truth to that, but it's also somewhat par for the course in Trek to add different layers to various cultures over time. Even the otherwise steadfast Vulcans were revealed to not always have been so nice during ENT. And the Klingons went from sneaky tricksters to an honor-bound warrior society.
...Both cases allowing us to argue that nothing really changed. Vulcans were assholes in "Amok Time" and "Journey to Babel", and Klingons played dirty also well beyond TOS. But that would be selling the writers short, as they indeed added complexity to aliens originally created to serve a single dramatic purpose. They just didn't do it at the cost of the original characterizations.
It should also be remembered that Vulcans and Klingons were familiar to our heroes from way back even when first introduced. The Borg were alien. I'm a big fan of what was done to them subsequently - essentially, our heroes' initial assessment was proven categorically wrong, just as it should be. Despite Q's lies, the Borg weren't uninterested in people; they were merely uninterested in our heroes. Take that, Picard! Despite having babies in drawers, they didn't procreate; Q told them as much, but again in the form of a lie, as we later appear to learn that a Borg Drone doesn't exactly cease to be male or female for good, it merely stops manifesting those attributes much. The heroes even got the concept of the Collective all wrong, being unaware of such key nuances as the Queen or the Vinculum. And the thing is, they couldn't have known better, and definitely shouldn't.