Opening up a SavedVariables file from one of the addons with the not quite fancy green border and look for the texture path should help.
WTF\Account\<YOURACCOUNTNAME>\SavedVariables then look for the .lua file for one of the addons, for example you tooltip addon.
Example: I open up that folder, find the SavedVariables for my tooltip addon (TipTac) which is named TipTac.lua.
I then look through it and find a line that goes like this:
This line tells me what the texture name is, and it's location. I then open up said location
["tipBackdropEdge"] = "Interface\\Addons\\Quartz\\textures\\grayborder",
Interface\AddOns\Quartz\textures and find a .tga file called grayborder. Considering your not quite fancy green border, you should not be able to find said file in the location in the SavedVariables for your addon.
Or you could look up the name of the border texture ingame on one of your addons and search for it on your computer. I just like opening up those .lua files, makes me feel smart
Do note, it's not guaranteed you will find ["tipBackdropEdge"] in your SavedVariables if you're not using TipTac. Look for something that has to do with Edge or Border.