Clause 28 of the current version of the Bill says simply:
"Chapter 2 of Part 1 of the Local Democracy, Economic Development and Construction Act 2009 (petitions to local authorities) is repealed."
The explanatory notes confirm that the clause "removes the requirements for principal local authorities in England and Wales to make, publish and comply with a scheme for the handling of petitions made to the authority, and to provide a facility for making petitions in electronic form to the authority".
It is interesting that on the one hand the government is removing one consultation mechanism, plausibly in the name of decentralisation given that the 2009 Act seems pretty prescriptive, yet adding a requirement that a petition signed by five per cent of the area's population can force a council-wide referendum.
Anyway, Dave Briggs has a great post today on why local council ePetitions don't seem to have had much impact, and discusses some reasons why it might not be the end of the world if the requirement to host them is repealed.
I'd also recommend his spreadsheet looking at the outcomes from local ePetitions.