Thanks for reaching out to the UNH Extension Infoline.

The first step in managing a mole or vole problem is to make a positive identification.

Moles are subterranean insectivores (not rodents) that are rarely seen above ground. Often, the way you'll know you have moles is the existence of small mounds of soil in your lawn. UMD Extension fact sheet on moles.

Voles are rodents that resemble mice and feed on bulbs, tubers, seeds, roots, and bark. They tend to make tunnels in between snow and the surface of the ground. These tunnels are especially visible after the snow melts in spring.

Check out this resource for more information on identification- "Mole or Vole" UNH Extension

Moles, being insectivores, do not typically damage vegetable or ornamental gardens. They can actually help control lawn and garden insect pests while aerating the soil as they dig their underground tunnels. Voles, on the other hand, are more destructive to your gardens by feeding on flower bulbs, root vegetables such as carrots and potatoes, and will chew on orchard tree roots and bark.

If you decide that control is needed, trapping these critters is the most effective method. For voles, a simple mouse trap baited with apples and placed near their tunnels can work well. For moles, try to find the freshest mound or mounds, step on it to flatten it out and then see where the soil pops back up the next day. That will tell you that there is an active mole nearby. Place multiple harpoon-type traps nearby the active tunnel.

You pictures appear to show vole activity. If you  do not wish to trap then create a solution  of 1 cup of caster oil, 4oz dish soap ( eg Dawn) to one gallon of water and spray into the holes. Repeat as needed. Also try ringing your vegetable garden with marigolds and onions as a further deterrent.

The use of buried hardware cloth is also effective.

I trust this helps.