Question about oak branches

[Ambermai]

Hello! I was wondering how much bark I need to strip off an oak branch to make it bird safe? I have just taken off the surface-level bark, will it be ok for my fids to chew? I put them on once and they immediately started to chew so I want to make sure it's safe.
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[getwozzy]

I would strip ALL the bark- down to the wood.

Btw- oak is one of those woods that's "safe" on some lists (wood only) and "unsafe" on other lists.