Since you found standing water in those urns and knowing the weather forecast for our weather is for on and off rain until the weekend, I might be inclined to scoop them out and put them in a temporary pot in dry soil under a table or something that can keep them out of the rain for a bit. Petunias rot way too easily, where the bottom leaves will start to yellow and the stems can eventually dampen off. :-(

Then consider doing something to help your urns drain. Did they have a drain hole? I noticed that many plastic or resin containers like that including the troughs, have plastic plugs over the drain holes that you'd have to remove if you want it to drain (I'm guessing they are there to allow the containers to be filled with water too, so that option is made available). Ceramics sometimes have a plug blocking a central hole or may have no hole at all.