They promise to keep an eye on the house for us.
点睛
keep an eye on sth. 意为“照看;密切注视”。如：
It isn't easy to concentrate on your work when you've got to keep an eye on a baby who is crawling all over the places. 当你要分心照看一个四处乱爬的婴孩时，就不容易集中精力工作了。
考点归纳
与keep有关的口语短语还有：
keep body and soul together意为“勉强维持生活”。如：
He is so poor that he cannot keep body and soul together. 他穷得连温饱都不能保证。
keep it to yourself意为“保密”。如：
You should keep it to yourself—otherwise you'll be in big trouble. 你要保密——不然你就会有大麻烦。
keep my fingers crossed意为“交叉手指;祈求某事成功”。如：
I will keep my fingers crossed for you today. 希望今天幸运之神眷顾你。
keep one's head above water意为“活下去;不负债”。如：
Earning barely enough to support the family, father was quite happy only if he could keep his head above water. 父亲赚的钱勉强够养家，能不欠债就算不错了。
keep one's shirt on意为“要保持冷静”。如：
Keep your shirt on, Harry; we have plenty of time to catch the train. 哈里，别太紧张了，我们还有很多时间，足够我们赶到火车站的。
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