Machinae Coelestis chapter XXI discusses the long telescope in detail.
Fortunately C. L. Prince's 1882 English translation is online via HathiTrust.
The square boards with round holes are baffles to keep the eyepiece field free of unfocused skylight, with structural reinforcement as a secondary benefit.
From pages 41-42 of the translation, apparently referring to Figure Z in the Latin:
On the other side of the upright plank (a a), as may be seen at A and D, i.e., on the side opposite to the supports and braces (c),
I placed square boards (d), also at right angles, about a foot square, having a large hole bored through them...not only with the view of giving additional support and strength to the planks,
but principally...entirely to exclude all light from the outside, which might fall on the lenses or dazzle the eye of the observer.
From pages 51-52:
You will perhaps exclaim, "...in what way, I ask, is the entire instrument and its intermediate parts to be closed up? Will the instrument you have described perform its duty, being quite open on all sides?"
I reply that the instrument is certainly not a perfectly closed tube, yet nevertheless it does the duty of one quite as well as if it were really covered in on every side;
for since the square perforated boards are not more than three or four feet apart, they totally exclude light from the lenses and from the eye of the observer, so that when you apply the eye to...the first hole, you will see nothing but the tube in complete obscurity, and at the end a perfectly round hole;
for all the perforated [boards] are completely blackened on the side turned towards the observer, so that you catch nothing but the tube with its veil of blackness.
Hevelius further explains that the holes near the observer are narrower than those near the objective, but not so narrow that a slight bend would induce vignetting.
He does not mention a lens in any of these holes.
Modern refractors, in addition to a closed tube with a blackened inner surface, may employ multiple baffle rings to hide that surface from the eyepiece.
Here is such a baffle assembly before installation in a DIY refractor:
Source: Dick Parker