The phrase "quickly grabbed" is grammatically correct and can be used in written English.
Example: "She quickly grabbed her coat and rushed out the door before anyone could stop her."
The subsequent police crackdown triggered nationwide protests, which quickly grabbed the world's attention.
They quickly grabbed me for a role that was development but also sales.
I quickly grabbed my sheet and flicked it, repulsed that the roach was in my sheet.
Low-cost broadband telephone services have quickly grabbed 10percentt of the market in Japan.
We waved, and a few small children waved back, but they were quickly grabbed by their parents and stopped.
The painter quickly grabbed the bag and rushed down the steps to avoid seeing the kindly tenants.
That is partly because it is in office, but also because the Tories' leader, David Cameron, quickly grabbed the initiative.
Frazzled and running late after the lengthy search, Mr. Strasser quickly grabbed his belongings and rushed to his gate.
McKee Nelson burst onto the scene in 1999 and quickly grabbed lucrative Wall Street work from long-established rivals.
He quickly grabbed his son, family and friends and piled nine people into a walk-in freezer until the storm passed.
