Are you expecting no overlaps? Perhaps try BEDOPS, in order to see what answer you get with an alternative toolkit.

First, sort the inputs:

$ sort-bed ProE_replicatePeaks.unknownSortOrder.bed > ProE_replicatePeaks.bed 
$ sort-bed 1kbTSS.unknownSortOrder.bed > 1kbTSS.bed

Then do the exclusion operation:

$ bedops --not-element-of 1 ProE_replicatePeaks.bed 1kbTSS.bed > ATAC_Not_Pr.bed

You could also do the opposite operation:

$ bedops --element-of 1 ProE_replicatePeaks.bed 1kbTSS.bed > ATAC_Pr.bed

In theory, if the first operation worked in the same way, you would get one BED element from the second operation, with which you can do a sanity check by comparing 1kbTSS.bed with ATAC_Pr.bed:

$ bedmap --echo --echo-map 1kbTSS.bed ATAC_Pr.bed > sanityCheck.bed