Both the below options work well.
$ zgrep -ai 'CDF_FEED' FeedService.log.1.05-31-2019-150003.tar.gz | more
2019-05-30 19:20:14.568 ERROR 281 --- [http-nio-8007-exec-360] DrupalFeedService : CDF_FEED_SERVICE::CLASSIFICATION_ERROR:408: Classification failed even after maximum retries for url : abcd.html
$ zcat FeedService.log.1.05-31-2019-150003.tar.gz | grep -ai 'CDF_FEED'
2019-05-30 19:20:14.568 ERROR 281 --- [http-nio-8007-exec-360] DrupalFeedService : CDF_FEED_SERVICE::CLASSIFICATION_ERROR:408: Classification failed even after maximum retries for url : abcd.html