Origianlly, the term "screw the pooch" was -- feed the dog OR feeding the dog. Later, it was militarized and it became f*ck the dog -- meaning someone messed up what they were supposed to do. Finally, a writer -- in his book changed the term -- "F*ck the dog" to "Screw the pooch" so It can be used in a general conversation and wouldn't offense anyone

Screw the pooch only means not doing what they were supposed to do or doing a very lousy job.