there is a problem on the corner of the exterior

What is the problem?

The problem to me looks like the gutter is not emptying into the downspout, but running down the brick wall and causing algae growth. I would get your gutter guy out to fix it. Wet & Forget (buy at Lowe’s) will help with the algae.

I would have someone snake your downspout to make sure it's not clogged. Also make sure your gutters are not improperly sloped toward the brick wall.

I made sure of and we put the gravel under a mesh around the entire perimeter of the house. But do you mean is there foundation under that gravel that the brick is on?

I think that worthy is asking if the downpipe is connected to underground pipes that divert the water away from the foundation. Your downpipe should be attached to a drain pipe underground (ideally seated in gravel) that takes water either to the street where it can reach a storm sewer or to a rain garden.

If you had the gutters recently installed, I would have the installer come out and look at your issue and ask how the downpipe system works. When it is raining do you see water coming over the side of the gutter all along the length or is it just coming out at the end? Take a video of it to show your gutter pro.

It's possible the drainpipe is backed up and sending water back up to the gutter where it is running over the end. But it looks to me like a pretty constant drip to have the algae growth like that (unless this is the north side of the house, which wouldn't require constant moisture). My guess is that the water is coming out that terminal end of the gutter (and by-passing the downpipe) because it isn't sealed properly or it's running off the roof and there is no flashing there to divert it away from the house.

Blocked downpipe:

Buried sloped pipe running to a rain garden:

Buried pipe in gravel: