No MQ tags in VCF files
As @ATpoint explains in his comment, the mapping quality (MQ) applies to read mappings and, hence, is contained in BAM files, but not VCFs. The MQ values carry important information that ideally the variant caller should use when determining the variant quality (QUAL in the VCF) of individual variant loci.
In the LoFreq documentation it says that

Choice of mapper: Bowtie and BWA-SW
BWA-SW assigns very low mapping qualities to mapped reads. LoFreq incorporates mapping quality by default into its variant calling model, which doesn’t help in this scenario and will reduce its sensitivity. Consider disabling the use of mapping quality for lofreq call with -N.

So LoFreq is already aware of the MQ values and takes them into consideration during variant calling.
Since you are using BWA-MEM (and not BWA-SW) you should probably not be concerned about the issue they mention and trust their quality filtering.
If you are sceptic about the quality of mappings, though, you could still filter them out directly after mapping, e.g. using samtools view -q 20 ...