TekRing is a small part is placed over the BNC connector just before the probe is snapped on. This thin ring, with it's very tiny resistor circuit, is squeezed between the readout ring and ground, providing the correct value to the scope. Note there are two versions of the ring (and two colors), for 10x (brown) and 100x (red) probes.
The TekRing is just slightly larger then the diameter of the BNC connector. In place it's hardly noticeable. They are two colors, brown for 10x and red for 100x. This ring provides the correct resistance signaling the scope to change it's vertical value. It does exactly what a Tek probe does, that has a readout pin, except "externally". It does not make your probe any "better" so a cheap low bandwidth probe, is still a cheap probe. But you will have the correct values (V/div) displayed on the scope