Recently the CERN ALICE experiment, in its dedicated cosmic ray run, observed muon bundles of very high multiplicities, thereby confirming similar findings from the LEP era at CERN (in the CosmoLEP project). So far their presence is still not fully understood. We propose as a possible explanation of this phenomenon that they could be produced by strangelets, hypothetical stable lumps of strange quark matter infiltrating our Universe. We also address the possibility of additionally deducing their directionality which could be of astrophysical interest. Significant evidence for anisotropy of arrival directions of these strangelets is found. Estimated directionality suggests their possible extragalactic provenance.