There are a few ways that you can clean the inside of your leather gloves, depending on how soiled they are.
If they are only lightly soiled, you can simply wipe them down with a damp cloth.
If they are more heavily soiled, you can spot-clean them with a mild soap and water solution.
Finally, if they are very soiled, you can machine wash them on a gentle cycle.
Always air dry your gloves after cleaning them to prevent damage.