Should the drywall be removed? No. In fact, it’s common practice in a replacement window application that the drywall is not disturbed. This is the benefit of a custom-sized replacement window because it is manufactured to fit the existing opening, including any allowance for the drywall.
There are no studies and no indications that there are any chemical reactions or toxins being emitted when vinyl is introduced to drywall. Vinyl emits some off-gas, like all solid materials do, such as new carpet or paint, etc. but not enough to make you ill.
It could be the smell of the caulk, or the urethane seal. That smell could possibly make you feel sick, until the caulk, etc. cures.
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