To the best of my knowledge, Janice is not a word or a name in Hebrew. (Hebrew is my mother tongue)
After short research through babies names websites, I understood that they group the name Janice with other, similarly sounds, names such as Jane and associate them with the meaning 'God's grace' in Hebrew.
As an Hebrew speaker I find it's possible but a little lose connection.
The word grace in Hebrew is חֵן (pronounced chen).
'God's grace' can be translated to חֲנִינָה (pronounced: chanina).
Like any translation, it is only one possible meaning of the word.
The word chanina, was used possibly to say 'God's grace' more commonly in old Hebrew (biblical Hebrew).
The translation is Gods' pardon, amnesty or mercy.
In modern Hebrew, chanina would be more commonly used as amnesty- a forgiveness for a sin committed, then as courteous goodwill.
The word Chen, which is the source of the word chanina, meaning is grace, charm, attractiveness, but, that wouldn't necessarily be associated with God.
In any case, I wouldn't think that an average Hebrew speaking person would think of those meaning when hearing the name Janice, but, I am not sure that this is of any importance to you.
for example: the name James comes from the Hebrew name Jacob.
Its meaning is "to track or follow". Biblical: the son of Isaac and Rebekah and twin brother of Esau. he was born second and followed Esau, his name came from the Hebrew word to follow/to tail- לעקוב la-aqov which it's source is the word עקב Aqev - a heel, because he came to the world second following Esau heal/trail.
In Hebrew it will be pronounced Yaakov.
When an Hebrew speaking person think of the English translation of the name Yaakov it would be Jacob rather than James, despite James academic connection.
While girls name like: Hannah/Ana (Chenah), Eve (Cheva), Abigail (Avigail), Judith (Yudit), Ruth (Ruth) etc kept the clear connection to the original name and therefore to it's meaning in Hebrew.
I hope that this help.
Jane, Janet, & Janice derive from a Hebrew name that means "God's grace."
from the site: http://pregnancychildbirth.suite101.com/article.cfm/baby_girl_names_that_begin_with_j
those are few other website with more information on the name Janice
http://www.thinkbabynames.com/meaning/0/Janice
http://babynamesworld.parentsconnect.com/meaning_of_Janice.html
a good website for English/Hebrew translations:
http://www.melingo.com/rav_lan.htm
more info on 'God's Grace':
http://en.allexperts.com/q/Hebrew-Language-1605/God-Grace.htm
Hebrew baby names page:
http://www.babynology.com/hebrew_babynames.html
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