Generally, what causes low read mapping efficiency? Some samples have 70% and others are 8-20%. I am experienced with bowtie2 and tested with/without trimming. These are human and mouse cut&run.
We are not confident in the antibodies used, but I thought bad antibodies would lead to no peaks later on rather than low alignment.
No magic bullet here. Get representative reads that do not map and investigate with BLAST. You may have some unexpected contamination.