Hey Cowboy,
I might not be telling you anything you don't already know because I don't know anything specific about the Delta brand name. So, if that's what you wanted, you can stop reading now.
It is an Hutchinson soda bottle. Probably dates somewhere around 1900 (give or take about ten years). It has a mug or faceted base which was not unusual for those bottles. It was originally sealed with a metal stopper that was shaped something like a question mark with a rubber gasket at the bottom. They are pretty collectible but the value is determined by the rarity, condition and other factors. I've never heard of Greenville and that could mean it is from a small town - which is almost always a good thing. I also think that collectors will like the diamond design on the front and bottom. Hope this helped. Sorry if it wasn't what you wanted.