When I recheck a document on Paperpal for Word or Web, is there a way to avoid getting suggestions that I didn’t accept from the previous check?

Yes. If you don’t want a suggestion to appear in subsequent checks, just make sure that you actively “Reject” it on the suggestion card. Paperpal tracks the document ID, so as long as you’re working on the same document in a subsequent round, the tool will not provide suggestions on sentences that are already actioned once.