Pressure Dressings After Transconjuctival Blepharoplasty?

There should be no reason to use a pressure dressing underneath the eyes after lower eyelid surgery. Perhaps your surgeon just meant cold compresses, not compressive dressings per se.
If bleeding should occur, it might be trapped in a tight space, or go unrecognized. This could lead to very damaging pressure on the eyeball and optic nerve.
Usually doctors recommend ice, elevation, decreased activity postoperatively. Surgery should be carefully performed, to minimize bleeding. The patient should be medically optimized before surgery, to reduce the chance for high blood pressure (a leading cause of bleeding). The surgery should be performed in a monitored setting in an accredited surgical facility, to see if potentially dangerous early warning signs of changes to the vital signs are there.

Some surgeons blindfold their patients overnight to keep pressure on the eyelids and minimize swelling.  Either pressure bandages or cold compresses are acceptable.  Choose whichever surgeon you are comfortable with and follow their directions. I  personally place pressure bandages on my eyelid patients for about an hour after surgery but remove them prior to sending them home.

There are many other ways to minimize bleeding around the eye other than pressure that tend to be preferred by surgeons. Some of these include:

Avoidance of blood thinner medications preoperatively
Good intraoperative technique and hemostasis
Control of blood pressure
Pain management
Head elevation
Ice compresses
etc.

Having read my well-trained and experienced colleagues comments, I agree with the basics of what they have said. However, I suspect that what your surgeon may have proposed, and what I frequently do myself, is to place a moist cotton dental roll on the lower eyelids with a horizontal piece of paper tape to hold it for about 24 hours.

This provides a minimal amount of pressure and seems to decrease the amount of bruising. The incision with a transconjunctival lower eyelid blepharoplasty is typically not closed, so bleeding, should it occur, would still leak out of the open incision. My suggestion is that you speak with your surgeon to further clarify the issue.

Dear Annabel
There is absolutely no reason to patch the eyes after blepharoplasty. Patching will not prevent orbital bleeding after eyelid surgery but it will make it more likely that you can go blind if your suffer bleeding following surgery. A very important sign that prompts immediate post operative re-assessment by the surgeon is loss of vision after surgery. If your eyes are patched after you cosmetic eyelid surgery, you will never know if there is a problem with the vision. I should stress that we are talking about rare events. So it is possible that your surgeon has gotten away with a bad habit simply because he has yet to experience an orbital hemorrhage after surgery. However, this is such a profound departure from what reasonable surgeons do I would strongly recommend that you find another surgeon. This is a red flag.