Step 1: Recall what an adverb does.
An adverb modifies a verb, adjective, or another adverb. It answers questions like how, when, where, or to what extent.
Step 2: Analyze each option.
Committee is a noun, approved is a verb, and strong is an adjective modifying objections. Only reluctantly modifies the verb approved by telling us how the committee approved the proposal.
Step 3: Confirm.
Reluctantly ends in the suffix -ly, which is a common adverb marker, and it clearly describes the manner of the action taken.
\[ \boxed{\text{reluctantly}} \]