I have come across this issue before in other projects, and I just move the light around, so I cannot see the reflection emitted from a light source. I have seen videos like this https://www.youtube.com/watch?v=9IjEXE70ujI go to time 1:25. But when I try it, nothing disappears. The only way I am able to get the reflection to disappear is if I uncheck transmission in the ray visibility section. But I have found that if I'm working with anything transparent, then the light doesn't go through the object anymore. As you can see the glass ball has light going through it landing on the P key, but I can see the light source in the reflection, and after I turn off transmission it will disappear, and you can see the window now but the hint of light that was passing through the glass also disappears.
Scene setup is a glass ball with Principled BSDF, Transmission of 1, an area light, and a primitive plane.
Here's rendered view:
You can add a plane with a Transparent BSDF between the glass ball and the object to have light cast on it, in this case the floor.
Then set your light to Use Nodes.
In the shader graph we can specify that for a Transparent Depth less than one (.9 actually, non-inclusive?) we emit no light.
Now we can see that the plane is giving us some problems, so we have to disable Camera ray visibility for the transparent plane.
What this leaves us with is basically all of the light that goes through the plane, and it's taken the light source out of the glass.
With a slight modification we can take out that giant white chunk at the top, and I believe we've mostly achieved the goal. You should have decent control over where the refracted light is allowed to show.
To get the effect you want in your scene you might have to crank the wattage up. We're totally torturing this light, so any arguments about conservation of energy went out the window long ago anyway.