bava kama 9b - Hiddur Mitzva

There is a famous chakira about the din of hiddur mitzva, זה א-לי ואנוהו if it is a separate halacha we apply to mitzvos or if it is incorporated into the mitzva itself. Rav Soloveitchik explained that this chakira explains the two side of the question in our gemara of the 1/3 hiddur is מלבר or מלגיו. He explained that if we say that it is part of the mitzva, then it makes sense that when we look at the chefza you have at the end, that 1/3 of it be hiddur, thus it would be מלבר but if it is just a separate halacha then using what you have now, you tack on the hiddur of 1/3