The link results in a single-point ground. If there were more than one point of grounding of the core to the tank or other structure, then the result would be the equivalent of a shorted single conductive (more or less) turn within the magnetic path of the transformer. This would result in a high current flowing through the resultant path, and usually shows up as heat and unusual excitation current.
By using a removable link, the user can remove this link and test the core's insulation to ground to determine if a second, unwanted ground of the core exists.
If the links are left off, a charge may build in the core in relation to ground. When it reaches sufficient voltage, it will "punch through" the core to ground insulation. At the very least, this results in some unexpected gases in the oil during your periodic analysis. At the worst, it can deteriorate the oil, and carbonize enough material to result in a full-blown fault of the transformer.
old field guy