In the GC manuscript, Tasso was uncertain between "è da Gran Re Norvegi," like in Gerusalemme Liberata, and "fu da Gothi Regi" (descended from Goth kings) as it will appear in the final printed text. What remains unaltered is the Nordic origin of the character Gernand, while Richard ( = Rinaldo in GL) turns from being the forefather of the Italian Este family to a Norman knight whose ancestors also came from Scandinavia. So, Tasso succeeds in moving Norse warriors to the Middle East, recreating the geographic setting -- Norway, Sweden, and Gothia i.e. Finland -- of his Shakespearean tragedy Il Re Torrismondo in his last masterpiece. Besides, the era of Il Re Torrismondo was the seventh century, in countries that were not clearly described as pagan or Christian, precisely like in Beowulf.
And why is this? Gerusalemme Conquistata, unlike the still basically Ariostesque Liberata, is a modern 'pulp' story, in which the combats often look like having been written by Robert E. Howard. To be sure, many battles come from Homer and Virgil, but Tasso adds further violence and gore. No more elegant duels but splatter. In fact, we will soon see Richard go berserk.
The reason why Tasso expunged the Ferrarese Este family from Gerusalemme Conquistata obviously was a 'thanksgiving' for the 'treatment' -- to internalise him in an asylum -- they had subjected him to.