You probably have the peak coordinates and then used something like bedtools getfasta. What you can do is to first identify the genomic coordinates of these repeats, e.g. using any of the solutions from A: Code golf: detecting homopolymers of length N in the (human) genome (modified to match these tandem patterns you encountered) and then use these coordinates to filter out any peaks that intersect with these blacklisted coordinates e.g. using bedtools intersect. Then get sequences from the remaining peaks and re-run the motif search.

Seems like dust might be a helpful tool for this. You could also browse the excellent MEME suite Q&A page or post your own question there.

Try GimmeMotifs. It combines different motif prediction tools (including MEME) and compares the identified motifs to a background set of sequences. It usually work very well for ChIP-seq data (disclaimer: I wrote the software).