It seems that "fudge welt" is a term used by Edward Green for what is commonly known as "storm welt".
A storm welt is a band of leather which is sewn into the interface between the shoe's upper and the sole. It is suppose to keep water (hence storm) from getting into the area where the upper meets the sole and soaking into the shoe. It does help make the shoes more water resistant to some extend but it is not as effective as stitchdown construction, which are commonly used in heavy duty boots, which seals the boot against dirt, mud and water. High quality mountaineering boots use the stitchdown construction while storm welts are traditionally used on military boots.
I guess the "fudge welt" here could be there for decorative / design purposes more than its functional purpose. Having said that, it does give these monks an added level of casualness.
Hope what I wrote makes sense.
Gaz