At-Tatawwu' ( اَلتَّطـَوُّعُُ ) is derived from at-taw'...
In short, at-tatawwu' is not reserved, from the linguistic point of view, for voluntary, non-obligatory good deed - unless credit is given to the usage of the common people. Commentary Qur’an: Surely the Safa and the Marwah are among the signs of Allah... to go round them both: The two hills are marked by the signs of Allah; they lead accordingly to Him and remind one of Him.
They have been especially counted “among the signs of Allah” to the exclusion of other things; it shows that the word, “the signs” has not been used here in the sense in which every created thing is a sign of the Creator. They are the Divine Signs because Allah has made them so, by appointing them as the places of His worship; thus they remind one of Allah, the Creator. They are the signs for which Allah has prescribed especial rites of worship.
Then comes the next sentence: “so whoever makes a pilgrimage to the House or performs 'umrah thereof, there is no blame on him to go round them both. The word “so” in the beginning shows that it is an offshoot of the preceding sentence. Its import is to show that walking quickly between these two hills is a part of the Islamic shari'ah - it does not imply that the said walking is voluntary or non-obligatory.