This is an ongoing debate. Personally, I've never seen anything that suggests to me that they are genuine, in fact exactly the opposite. Leaving aside this one, In the case of the two towers pieces, I find it inconceivable that they would make a series in penny increments all the way from 6d to 1s4d plus the higher values. All that would be required would be to get approximately similar pieces of plate, weigh them, and stamp the value. It's not rocket science. You get an example or two of each denomination - which doesn't make sense.
Although the denominations seen on the castle and gateway types are more sensible, I also struggle somewhat from a perspective view, and think the castle may be viewed looking at the inside wall.
It is also important in my view that Cholmley is reported as producing coins to pay the troops, but no mention is made in connection with this of the quantity of CARA farthings found at the bottom of the castle well (cf. Peck p.56). Although there are pros and cons for them being contemporary with the siege, not least the fact that they constitute the early issues of copper farthings. When one considers the designs employed on some of the provincial civil war silver, they clearly hark back to the early part of Charles' reign, so it would be wrong to exclude the CARAs as possibly being made at Scarborough.
Although some of these pieces were in collections going back to the end of the 17th century, that still doesn't place them as being contemporary with the siege. I think it is significant that other siege pieces such as Newark and Carlisle were struck in towns, not just within a castle.
I had a discussion with kal about 3 and a half years ago on this topic. I laid my views out in a note, the contents of which are attached. I haven't changed my view on this since then. I'm sure kal will come back on this given his interest in the subject.
140731-Kal on predecimal discussion.docx