Есть ли причина, простой JavaScript Array.prototype.filter()
не будет работать для вас?
const src = ['05/20/2019 15:22:58','06/06/2019 16:42:19','06/06/2019 17:33:18','06/07/2019 18:52:09','06/08/2019 09:32:49','06/08/2019 10:25:02','06/10/2019 17:43:22','06/12/2019 19:03:22','06/15/2019 07:28:44','06/15/2019 09:19:34','06/15/2019 07:41:55','06/15/2019 09:57:29','06/15/2019 10:43:41','06/15/2019 11:01:06','06/15/2019 12:11:29','06/15/2019 11:59:45','06/15/2019 12:26:51','06/15/2019 14:20:59','06/17/2019 17:19:41','06/17/2019 17:25:46','06/17/2019 17:29:45','06/17/2019 17:30:49','06/17/2019 17:33:55','06/17/2019 17:07:52','06/17/2019 17:48:49','06/17/2019 18:01:09','06/17/2019 18:24:32','06/17/2019 18:28:32','06/18/2019 17:25:45','06/18/2019 17:37:30','06/18/2019 17:46:49','06/18/2019 17:51:23','06/18/2019 18:05:15','06/18/2019 18:10:21','06/18/2019 18:21:09','06/18/2019 17:54:39','06/18/2019 18:00:57','06/18/2019 18:12:34','06/18/2019 18:13:49','06/18/2019 18:31:27','06/18/2019 19:14:11','06/19/2019 17:06:39','06/19/2019 17:34:16','06/19/2019 17:37:25','06/19/2019 17:05:14','06/19/2019 17:18:30','06/19/2019 17:34:54','06/19/2019 17:43:17','06/19/2019 17:46:32','06/19/2019 17:48:10','06/19/2019 17:50:40','06/20/2019 18:47:59','06/20/2019 19:04:12','06/20/2019 19:09:11','06/20/2019 20:13:04','06/21/2019 17:18:22','06/21/2019 18:38:30','06/22/2019 07:41:11','06/22/2019 07:44:51','06/22/2019 08:16:10','06/22/2019 07:51:27','06/22/2019 07:55:30','06/22/2019 08:01:44','06/24/2019 18:00:12','06/24/2019 17:22:03','06/24/2019 17:23:59','06/24/2019 17:50:38','06/24/2019 17:56:12','06/24/2019 17:58:08','06/24/2019 18:03:22','06/24/2019 18:07:28'];
const res = src.filter(dateStr => (new Date() - new Date(dateStr))>7*86400000 && (new Date() - new Date(dateStr))<14*86400000);
console.log(res);