记不清 follows the potential complement pattern: verb + 不 + result. 记得清 is the positive form meaning "can remember clearly." This 得/不 structure is extremely productive in Chinese.
usage
Compare: 记不住 (can't memorize/retain) vs 记不清 (remember but not clearly). 记不住 means total failure to remember; 记不清 means vague, fuzzy memory.