EAST RUTHERFORD, N.J. -- It has been a costly first week of the season for the New York Giants. With the release of kicker Randy Bullock on Tuesday and starting middle linebacker Jasper Brinkley last week, they received four kickoffs and a missed extra point for what could amount to close to $2.5 million.

Bullock was cut one day after Josh Brown was reinstated to the active roster from his one-game suspension. Bullock signed a one-year, $675,000 deal earlier this summer.

As a vested veteran, he’s eligible for termination pay, and the full $675K salary he was due. He could collect the full amount -- and double dip -- if he lands on another roster over the final 16 weeks.

Brinkley signed a one-year deal worth $1.8 million with the Giants this offseason. He was guaranteed $1.7 million in base salary and roster bonus, and earned the other $100K in the form of an offseason workout bonus.

The Giants cut Brinkley last Tuesday after he lost out on the starting middle linebacker job to Kelvin Sheppard. Brinkley started nine games for the Giants last season.

To ease the financial burden, linebacker J.T. Thomas -- since placed on injured reserve with a torn left knee -- took a $1.375 million pay cut prior to the start of the season. So, in the end, the Giants recouped some of the lost funds.

The Giants could’ve signed or claimed a younger kicker or a veteran who had exhausted the one-time termination pay option and saved over $600K. But they thought Bullock was their best option on Sunday afternoon against the Dallas Cowboys.The Giants had Garrett Hartley, Shayne Graham and Cody Parkey in for tryouts over the past month.

Bullock had four kickoffs (three touchbacks) and made 2 of 3 extra points in the 20-19 victory over the Cowboys on Sunday.

Defensive tackle Montori Hughes was re-signed Tuesday to take Bullock's spot on the roster. Hughes was waived after final cuts when the Giants claimed defensive tackle Robert Thomas from the Carolina Panthers.