Без регулярного выражения:
String str = "The following images failed: [T430040.tif, T432040.tif, T411030.tif, CH1090.tif, T432050.tif, T432090.tif, T432020.tif, CRP040.tif, T432070.tif, T040060.tif]";
String[] array = str.substring(str.indexOf("[") + 1, str.length() - 1)
.replace(".tif", "")
.split(",");
System.out.println(Arrays.toString(array));
выведет массив:
[T430040, T432040, T411030, CH1090, T432050, T432090, T432020, CRP040, T432070, T040060]