I've always found the easiest way to work with times is to..... well, work with times.
If the times you have were real times rather than text, you could put this in F3 and drag across and down.
=IFERROR(IF(AND(F$2>=VLOOKUP($E3,$A$3:$C$7,2,FALSE ),F$2<=VLOOKUP($E3,$A$3:$C$7,3,FALSE)),"Yes","")," ")
see attached file.
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