Don't soak it in solvent; that will penetrate and overly dry the wood.
Just gently sand that stuff out with about 240 grit...
Don't steel wool either...the fine pieces can embed themselves in pores, etc...
You can sand that entire bow--lightly!!--including the glass just enough to prep it for a re-spray...and if done patiently, it will look like a pro job.
It's not that hard...trust me.
Do a search on Tradgang for Border and "bastard" and you'll see how I redid a complete Border Black Douglas riser, from taking a file to it, thru final sanding, and then had it re-sprayed.
Just be patient, patient, and patient. If it gets nerve-wracking, or you get worried, just put it down for the day and come back the next.
It'll be alright...
Take Care,
Marc