Mullein Moth?

[Lumpy]

I have these on my budleia's.

Do they eat veggies?

[cheops]

You can relax. No threat to your veggies. The mullein moth, Cucullia verbasci, lays its eggs on not just on mullein but they will also eat the leaves of figwort (the family of flowers to which mullein belongs) and buddleia.
If there are many caterpillars you can pick many off by hand otherwise they will not cause great damage to your buddleia.
As for the mueillin moth - it's not particuliarly attractive but has its place in nature so perhaps you and your buddleia and the mullein caterpillars can co-exist so that you are with nature and not against nature.

[Snoop Puss]

Sounds like they don't have many host plants, but they'll strip those few types of plant bare... Have a look at this for basic info:

https://en.wikipedia.org/wiki/Mullein_moth

[Jungle Jane]

I found one eating my grape leaves so I moved it to my Buddleia,it's made huge holes in the leaves but they are pretty aren't they.

[Lumpy]

As normal Thank You....................stripey pillars are still in situ.

[Martin H]

I had lots of these on my Verbascum this year. Last year too. I left them too it. They made a right mess of the flower spikes, but the plants bounced back and look OK again now.

[Lumpy]

This morning I saw a blackbird sitting on the fence where the plants are. Some have vanished but a few are still in place. I did look on the floor to see if a spat out caterpillar needed some help back into the plant but there was nothing there.