Identify the italicized (quoted) word or phrase.

"Putting" her sewing aside, she got up and answered the door.

The three possible answers are:

1.) participle

2.) infinitive

3.) verb phrase

The word putting is used as a participle in this sentence.

Participle is a verb form which looks like a verb + - ing. In sentences, participles are used either as adverbs (as is the case here), or as adjectives - depending on the context.

It's not an infinitive, because infinitives have TO + verb form (to put would be an infinitive), and it's not a phrase because you quoted only putting, not the entire phrase.