Welcome to the forums!

I would guess that the Moonlight template has two different logos, for sizing. One is used in the Website medium of the skin, while the other is used in the Tablet and Mobile mediums.
(I'm going on memory for the following, so bear with me...)
Open the skin associated with your target. In the skin editor's toolbar, you'll see buttons for Website, Tablet, and Mobile. Click the Tablet button. I'm guessing that you'll now see that smaller logo that came with the template. Click the Highlight button and then click that logo, so that the skin editor "jumps" right to the properties having to do with that logo. That's where you can change the image used.
The Mobile medium inherits its settings from Tablet, so you may not need to swap in yet a smaller logo. But in case you do, have a third image prepared, and then use the same process in the Mobile medium.
For more info, visit
https://help.madcapsoftware.com/flare2022/Content/Flare/Skins/HTML5-Skin-Styles/HTML5-Skin-Styles.htm.
HTH