There were two basic pre-modern views still present at the beginning of the 18th century:

1. starting with the antiquity there presumptions were made they are dealing with the petrified remains of extinct monsters (see «The First Fossil Hunters» by Adrienne Mayor)

2. Avicenna while explaining Aristotle suggested the fossils as evidence for that the earth is capable of creating life. He suggested we're dealing with embryo species and not with dead monsters. It was very popular in the middle ages and in 1702 it was still considered important enough to be brought up by Scheuchzer in Helveticae Curiosae along with the idea of distribution of marine life during the deluge. This approach lost a lot of weight in 1726 when the Würzburg professor Johann Bartholomeus Adam Beringer was pranked into publishing fossils inscribed with Hebrew as the authentic products of the soil.

Critchon is drawing a debate in late eighteenth century zoology between Georges Cuvier and Lamarck. Lamarck believed in the inheritance of acquired traits, i.e. that cats were descended from the "antediluvian monsters" by strenuous exercise and adaptation. Georges Cuvier, on the other hand, believed that organisms didn't change but went extinct and that complete new species appeared from time to time.

In the 1820s and 1830s a plenty of huge dinosaurs were found (f.e. by Mary Anning) which strongly undermined the theories of Lamarck. The argument brought up by Critchon may well've been uttered by some very Christian Lamarckist.

source: History of geology and palæontology to the end of the nineteenth century by Karl Alfred von Zittel.