The group accessed the land on Saturday evening just days after the clear-up was completed from the last time they were on the park at the end of May.
It is thought they are the same group of travellers who set up camp at Shelf Park earlier this month.
The Councillor team for Hipperholme and Lightcliffe Ward - George Robinson, David Kirton and Joe Atkinson - have discussed what measures can be taken to remove the travellers as soon as possible with West Yorkshire Police and Council officials, but are frustrated that the process to do this is complex and takes a substantial amount of time.
They have also requested an urgent meeting to discuss what measures can be put in place to secure The Stray for the future to prevent unauthorised access in the future.
The Councillor team were on The Stray and met with the Police as soon as reports were received that travellers had returned. In their request for urgent action, they set out the ‘frustration and anxiety’ of the community and ask for a discussion of ‘preventative measures to prohibit unauthorised access’.
Now, residents and businesses are being invited to give their views to support the Councillor team in their discussions with the police and council officials, including sharing what measures they would back, such as additional tree planting or physical barriers.
Views can be submitted at www.tellyourteam.co.uk.
Councillor George Robinson said: “I share the anger of the community that somewhere that is used by so many individuals and families every day has been taken over by travellers once again – especially coming so soon after we had completed the clear-up of the last time they set up camp on The Stray.
“As well as taking the steps we can to remove them as quickly as possible this time, we need to take action to prevent unauthorised access onto the land in the future. As your Councillor team, we have asked for an urgent meeting because we think there is more that can and must be done.
“To help us make that case, we would welcome your views so please go to www.tellyourteam.co.uk and share what you think should be done. Thank you.”