Neither the well digger nor the customer would know why one vs the other.Well. maybe WD but there is no reason to spec grounded delta.
I would strongly suggest that if in fact you needed 480v 3ph3w that you opted for a 480v 3ph4w wye. You ground the neutral (X0) connect your EGC at that point and bring it along with your (3) lines to the load. No need for a neutral. The benefit of this arrangement is instead of 480v to ground you no have reduced that to 277v which is a big difference.
It is not uncommon for it to be assumed that just because your 3ph load does not require a neutral and only 3 line conductors it can be mistakenly called a delta.
So you understand what I'm referring to this is a brief explanation of the used for a delta configuration which is not applicable in your application:
With a delta it is not uncommon for a plant that has a continuous process that can't be interrupted to be supplied by an ungrounded delta because of an OCPD tripping as a result of a ground fault incident and causing thousands of dollars in damaged material and equipment. With this type of system it is imperative to have ground fault detectors an alarms as well as being supervised a qualified person who would be able to address the grounding issue promptly. This is not applicable in your situation.
Otherwise the delta would be corner grounded (grounded 'B' phase). Grounding is important as it provides a current path back to the source should an ungrounded conductor fault to ground. As such it allows the OCPD to trip and clear the fault. But guess what, any line to ground fault will be 480v. Being that a GF would amount to 480v this would not be the best thing either if you had the option for 277v.