Reed Switches use an alloy of Nickel and Iron with a few other elements that make the alloy Ferro-magnetic and having a low Remanence. This is important, as this feature is what makes a reed switch work well. When a magnet is brought near, the reed blades become flux carriers of the magnetic field and take on opposite polarities and attract each other, to close the reed switch. When the magnet is removed, the alloy does not continue to hold an magnetism and the reed switch opens.
But when a reed switch is fixed near parts that are Ferro-magnetic, such a mild steel screw, jigs or fixtures, these parts also get magnetized by an external magnet but do not lose this magnetism when the magnet is removed. This means that they continue to affect the working of the reed switch, however mild the effect may be.
As a result, when a magnet approaches the reed switch, these parts also shunt the magnetic flux lines away from the reed switch, and as a result, there is not enough magnetic field to actuate the switch. Another possibility is that the other ferromagnetic parts in the vicinity could get magnetized to such and extent, that they keep the reed switch closed, even after the magnet has moved away. This is the reason, it is not recommended to use Ferro-magnetic mounting parts or screws within a 100 mm vicinity of a reed switch as it will reduce or alter its operating distance.