When compressing a file in order to upload to NOMAD, I am receiving an error that reads “failed to clean up compressor.” 
I am not sure, if I can answer your question. Maybe https://stackoverflow.com/ or similar sites give you better answers to tar questions.
I am not sure, why you quoted the “-”. You should also name the compressed file “*.tgz”. But neither should cause the error. Maybe its something inside your directory.
Typically this error comes up, if try to put the tar file itself inside the tar. But it is not obvious if and how this happens here.
If course you can also try to use zip: zip -r upload.selfAssembled.zip ./Self-Assembled-Peptide-Absorption-Spectra/*
I probably misspelled your directory. Please consider to copy and past shell output in the future, because I cannot copy and paste from your screen shots.