If it is PVA glue, saliva works quite well to remove it, but the act of removal can cause localized polishing of the finish.
I normally color the ends of the miters with a solvent (alcohol) based pigmented art pen prior to joining. Care taken to avoid getting the inks on the surface, but if you swipe it quickly with a soft cloth of a finger, it can be removed. I use Copic markers for that.
The glue is best dealt with immediately after joining by cleaning of excess with a dampened soft cloth before it has a chance to set.
After the fact you might try gently wiping with Acetone (all precautions exercised) to restore the matte finish. It may not work.
There are scouring pads available in the US under the brand "Mr. Clean". They are a soft foam and framers here have had some success using them to detail matte finished framing.