Okay, a little background to help you understand the issues here:
The purpose of the EGC (ground wire) is to bond together all the metal things that should not be energized by electricity, and if they do get energized, cause the breaker to trip. To do the latter, a hot connected to the EGC needs to complete a circuit. That is done by a single connection between the EGC and the grounded supply conductor (the neutral). However, any EGC system should have only one connection to the grounded conductor; if there is more than one connection, then that means some normal grounded conductor current will flow on the EGC (current will take all paths). And the EGC should not be carrying any current under normal conditions (if it does, it's called objectionable current).
A service from the power company has no EGC. So the EGC is established at the main service disconnect (the upstream most breaker) by having a single EGC-grounded conductor bond there. In your last picture, that green screw to the right of the right yellow plastic piece is your EGC grounded conductor bond. The grounded conductor bus is otherwise insulated from the panel cabinet, but that green screw goes through the bus, through the insulator, and screws into the back of the cabinet.
The modern way to run a feeder between structures is to include the EGC with the feeder. Then in the structure being supplied, the main panel there should not have a bond between the EGC and the grounded conductor. The EGC system in the building supplied is just an extension of the EGC in the supplying structure, and you don't want a second EGC grounded conductor bond.
However, an older way to run a feeder between structures was to omit the EGC in the feeder. Then the feeder at the supplied structure is treated like a service, where a new EGC system is established in the supplied building via an EGC grounded conductor bond in that building's main panel. The new EGC system and the supplying structure's EGC system should have no direct connection to each other. If they did, you'd again have multiple EGC grounded conductor bonds, causing objectionable current.
Hence the restriction for buildings supplied by a feeder without an EGC, that there be no other metallic paths between the supplying structure and the building. Because if there were, e.g. a water pipe, that water pipe would be bonded to the local EGC system at each end, causing the EGC systems to be interconnected. So that's something to watch out for, where you have an existing structure compliantly supplied by a feeder without EGC, and someone later comes along and adds a metallic water supply to the building. When they do that, they should also upgrade the feeder to include an EGC, and remove the grounded conductor EGC bond in the building's main panel, but they may not realize that.
One more thing to be aware of is that each building (except outbuildings fed by only one branch circuit) is required to have a grounding electrode system. If the building is supplied by a feeder with EGC, that grounding electrode system is connected to the EGC; if the building is supplied in a way that requires a grounded conductor EGC bond in the main panel, it is often instead connected to the grounded conductor in the main panel (which may not be a real distinction, often there's just one terminal bar serving both).
In your first picture, the solid bare conductor B is your grounding electrode conductor (GEC), it's not part of the feeder to the building (99% sure). In which case that panel should have a grounded conductor EGC bond in it. I can't tell if it does, is one of the screws through the neutral bar just extra long so that it goes into the case? And what is that blob to the left of where B terminates?
Anyway, assuming we are correct that the feeder to the outbuilding has no EGC, if you lift that GEC, the only connection between it and the EGC at the pole/house should be through the earth. So if you took a resistance measurement, I wouldn't expect anything lower than 25 ohms (which would be a very earthing connection). I'm not sure what the threshold is for your continuity tester, it might show that as continuity. But if you take a resistance measurement and get a low number like 1 ohm, that's a problem. Because most likely that means there's some other metallic path between the buildings, and the GEC is bonded to that path. [I assume the incidental contact between the case and the GEC as it exits the panel is not involved, but you could try wiggling it there to see if changes your measurement.] In which case the proper thing to do is to replace your feeder with a new feeder with EGC.
So that's the theory involved, and if I have a chance I'll look more closely at your pictures.
Cheers, Wayne