The word is biomedical and has been since at least 1921. At the start of a sentence, or in a title, it would be capitalised as Biomedical.
If some company chooses to use BioMedical as part of a brand, that's their business. It doesn't change the word as generally used, just as CinemaScope doesn't change the words cinema or scope as generally used.
The hyphenated bio-medical is also used, and if capitalised would be Bio-medical at the start of a sentence, but Bio-Medical in title-case.
At this stage though, the closed compound biomedical is well-enough attested that one is safer using that; hyphenating it my seem old-fashioned, bordering on twee.
Strike a red pen through BioMedical if it's not a brand. Strike a red pen through the hyphen of bio-medical only if you're enforcing a style-guide, as it isn't actually incorrect.