It looks like a small beak injury. It should heal naturally. Keep an eye on your bird and make sure they are eating as they usually do. If you notice changes in behaviour a vet consult is a good idea.
I also suggest looking at your enclosure critically, consider if there is anything that may have cause this injury. If your finch is only living with other finches this may be from something within the enclosure. Finches can get caught in bars, they can be pinched between clips, etc. If everything seems secure, don't fret, sometimes accidents, collisions and such can happen.
My last suggestion is to be careful how you hold your finch. Birds do not have diaphragms like humans, and they have very different biology. I will share an image to help you understand what I mean. I will also include a link on finch handling. You don't want to place pressure up into their abdomen. This can restrict their breathing since they are unable to inflate their air-sacs. Try to keep your finger running perpendicularly to their breast and avoid putting pressure on the soft tissue.
Here is a link with advice on handling:
Catching and Handling Finches
