Katie Holmes on July 06, 2012 in New York City. Credit: Wagner Az/PacificCoastNews.com

Staying strong for Suri Cruise hasn't been easy for Katie Holmes.

During a Thursday lunch outing to the whimsical, kid-friendly NYC eatery Alice's Tea Cup, Holmes put on a brave face for her six-year-old daughter with estranged husband Tom Cruise.

But the stress of her sky-high-profile split from Cruise, 50 -- the news broke exactly one week ago Friday -- was also apparent, observers told Us Weekly.

Looking noticeably thin in a backless halter top, Holmes was spotted having an intense, 15 minute chat on her cellphone in the corner of the restaurant as her two mom friends entertained Suri and other kids at the table.

The Jack and Jill star seemed "flustered and upset" as she spoke, hung up and then scrolled through her phone, one witness says; before returning to the group, the tearful-looking actress wiped her eyes and nose.

Coming back to the table, Holmes collected herself and gave a big smile for Suri and the two other children at the table. She treated her little girl to a star wand, book and feather headband at the restaurant's gift shop.

"Suri was extremely happy," another onlooker told Us. "She was looking at everything behind the counter and literally said, 'This is the best day ever!'"

Suri is at the heart of Holmes and Tom Cruise's impending divorce and custody battle. Holmes filed papers June 28 to end their five-year marriage, and took the unusual step of asking for sole legal custody of their daughter.

Indeed, a source told Us that Holmes (raised Catholic) and Cruise "fought viciously" over the bizarre tenets of Scientology parenting.

"She wants to be in charge of how Suri is being raised and didn' want her to have an exclusively Scientology education," one insider explained.