As I understand it a Grey import is a model not normally sold on the UK market by the official importer. A parallel import is a model that is offered by the official importer as well. For example my Thundercat is a parallel import as it was originally brought into the UK by an idependent importer rather than Yamaha, whereas something like a Suzuki Goose or Honda CBR400RR would be a Grey import as Suzuki or Honda Uk never offered these models on the UK market. As for insurance it shouldn’t be a problem if the bike is UK spec, but if it is a Grey they might be a difference. However, there a number of insurance companies that offer policys tailored to these type of bikes so you should be Ok if it isn’t something too wierd! Hope this helps!