The structure 看在…的面子上
"For the sake of..."
The structure 看在…的面子上 
indicates that an action is done for someone else out of respect.
In this structure, we should put the person for whom an action is being performed in place of the ellipsis.
indicates that an action is done for someone else out of respect.
In this structure, we should put the person for whom an action is being performed in place of the ellipsis.Scheme
看在
who
for whose sake?
的面子上
action
Examples
看在我的面子上，算了吧
Please, forget about it for me
kàn zài wǒ de miànzi shàng, suàn le ba
我是看在她的面子上才答应的
I agreed to do it for her
wǒ shì kàn zài tā de miànzi shàng cái dāyìng de
三位客人看在老人的面子上又坐下了
The three guests sat down again for the sake of the old man
sān wèi kèrén kàn zài lǎorén de miànzi shàng yòu zuò xià le