Field strength pretty quickly drops of over distance, and even the most powerful magnets don't go much beyond 100T (and even that's a stretch). Assuming you could somehow achieve 100T 1m away from the magnet (which is charitable, usually the high teslas are only achieved at the exact centre) then just a kilometre away it will have dropped to 1 microtesla, well below the 25~65 microtesla of the Earths gravitational field.

So you'd need those kinds of magnets on a kilometre spaced grid, which doesn't seem realistic. And that's with some rather charitable assumptions about building a strong magnet, to be honest I expect you'd have difficulty turning a few compasses in the same building, let alone miles away.

The AFRL press release linked in another comment says that this technique relies on measurement of the crustal magnetic field, which is in the 10s of nanoteslas range.

It depends on how far away they are. Magnetic (dipole) fields fall as the cube of distance. Since the earth's pole has a dipole moment (8.0 * 1022 Am^2) and is detectable ~30uT at the earth's radius, thousands of km from the core. Even a 1T field at a radius of 1m would be billion times smaller ~1nT a km away or 1/30k of the earth's field.

A giant 6T MRI would be comparable to earth's field at 27m.

They could using a small EMP weapon. These happen to have short range and are explosively pumped, so at that point it’s easier to just disrupt the magnetometer by initiating rapid explosive disassembly.

Based purely in my layman understanding of magnetism, you’d need quite a disturbance and that same energy would likely not make the rest of any electronics happy.

Also give away your position.

A static magnetic field would not influence nearby electronics.