That's the Lysimachia sawfly larva, not a caterpillar. I've always found sawflies easy to control with commercial insecticidal (horticultural) soap. Spray when you see that these insects are most active, avoid sunny days.

In some places Creeping Jenny is considered a noxious "weed" while other places and people consider it a good ground cover.
Sawflies, wasps not flies, probably will not "kill" your Creeping Jenny, although a large invasion of the larva can weaken plants so they are susceptible to other problems. Insecticidal Soaps can, when applied early enough in the life cycle, help control them and Insecticidal Soaps containing pyrethrins may be of some helps later, but then why use the soap since it is the Pyrtethrin that does them in. Spinosad also can be used but that is very toxic to bees (as is pyrethrin) so due care in use is necessary.

Here is a link that might be useful: Sawflies

bugs rarely kill a plant outright ...

and CJ is aggressive enough.. that i would not even bother eradicating them

besides the fact ... it will pupate very soon.. if that is near one inch ...

they will be gone soon ... and the aggressive plant will outgrow the damage ...

i wouldnt bother ...

now.. if it were a $100 conifer... i might go after them .. but not on this horribly invasive weed ...lol.. yeah.. i have a predisposition to hating CJ ...

it isnt worth the time, effort, nor cost.. IMHO ...

ken

Thanks everybody for your input, I really appreciate it!