Perhaps speakers of Am English may have difficulty answering this, because the lack of a word reflects the fact that the thing doesn't exist. But maybe it does exist....
They've stopped being used in the UK, but maybe the concept of 'crossing a cheque' still has weight. My first cheque book, in about 1970, had blank cheques that one could cross in ink - you drew two parallel lines from top to bottom and wrote "& co.' in the space between them. This had the effect of imposing a restriction on the recipient - it could only be credited to a bank account, and not simply exchanged for cash.
Shortly after that (mid-seventies...?) the banks started printing pre-crossed cheques. A while ago they stopped. Because of bank-laundering rules, you can't now exchange a cheque for cash anyway (unless you do it in the normal course of events at a bank because you hate ATMs ). So I don't think crossing has any force anyway.