"... a handful of people that tarnishes ..."

[Odessa Dawn]

She further added, "As a native of Jerusalem I know and respect this society. I know it's just a handful of people that tarnishes the reputation of an entire sector. I was very offended by what he did."
More: Soldier: Haredi man spat on me and my mother - Israel News, Ynetnews

"As for Newsweek's fate, the paid-digital strategy strikes me as little more than a face-saving move. I can't believe more than a handful of people are going to sign up," Kennedy said on his blog.
More:Newsweek ends 80-year print run, goes all-digital - Israel Culture, Ynetnews

The Young Professionals Program is geared towards candidates under the age of 32 who are interested in junior positions at the UN. Only a handful of Israelis have succeeded in passing its entrances tests over the past few years.
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Merriam-Webster's Learner's Dictionary

In sum, I don’t know whether a handful of takes singular or plural verb?

[SoothingDave]

It's plural to me.

[Odessa Dawn]

It's plural to me.

Great! Should I drop s?

"I know it's just a handful of people that tarnishes the reputation of an entire sector."

[SoothingDave]

I would. Some other native speaker might disagree. Collective nouns can be a matter of style or local preference.

[Chicken Sandwich]

In sum, I don’t know whether a handful of takes singular or plural verb?

***** NOT A TEACHER *****

I think it depends on whether we're dealing with a countable or uncountable noun. Consider the following sentence which I found in Google Books:

There is a handful of sand on the floor, and I fear someone will step in it and fall.
(The Inter-mountain Educator, Volumes 15-16)

I think that "are" would be less likely here.

However, in your sentence I would also use the plural form of the verb.

[Odessa Dawn]

***** NOT A TEACHER *****

a countable or uncountable noun.

I can add an indefinite articular an before uncountable noun, can't I? A countable or an uncountable noun, for example.

[SoothingDave]

I can add an indefinite articular an before uncountable noun, can't I? A countable or an uncountable noun, for example.

Yes, you could, but it's not necessary.