Doors – How to confirm that an exterior door is hollow core or solid core? And prove it to a skeptical father

My elderly father doesn't trust that his daughters know anything about home repair or maintenance. I keep pointing out that I've bought and sold 2 houses in the past 15 years, so I know something about it. They are ignoring my recommendations on GFCI outlets, but that's another matter.

Their realtor has told them that their front door is hollow core, not solid, and that he needs to have it replaced with a fiberglass door. It's also possible that he was listening to the realtor say that a fiberglass door would fix the binding lock in certain seasons and having to get a locksmith and misinterpreted the reason. Or the realtor thought chipping veneer was ugly and made up a reason to replace it.

It's a ~70 year old house, and they've had it ~35 years, so the door is at least 35 years old. If so, it survived the previous family having active boys. The door appears to be stained wood veneer. On the edges of the door you can tell that the wood is different for about a quarter inch on both sides. Something with minimal wood grain on the exterior or interior. Where the veneer, or the top layer of wood has come off, it's wood underneath.

The area where the lock was replaced with one shaped differently shows bare unfinished wood in the area that is exposed now.

So what is the least destructive way to conclusively confirm whether it is solid or hollow core? It is fairly heavy to open and close, but I may be comparing it to thinner, narrower doors that are also hollow core.

Also, because the door needs replacing, they are ignoring calling a locksmith, handyman, or letting me fix the deadbolt that is sticking. The door has had problems seasonally for decades. Sometimes you would have to pull the door hard in one or another direction in order to turn the deadbolt. This has gotten much worse since they replaced a broken lock. I think the new deadbolt is marginally larger than the old one, and the tolerances on the strike plate are too tight to accommodate seasonal swelling. Dad says the door keeps moving in one direction, but if it's doing that, it would have been doing it for decades and then the door wouldn't close. 1/8" motion for 35 years is 4 1/2 inches.

My proposed solution is to buy a larger strike plate, perhaps a quarter inch larger vertically and horizontally in the hole. Filing down the existing one would be an option, but its reinforced in two directions that would prevent that. I've got a Dremel clone, but am not sure which accessory would best file it down.