Green’s Dictionary of Slang

counter-caterpillar n.

[SE counter, a prison attached to a city court or a mayor’s office + caterpillar n.¹ (1)]

a constable.

1705–07

N. Ward Hudibras Redivivus II:6 9: These Compter-Caterpillars, / These Hawk-ey’d Shoulder-dabbling Dealers.