The 17,000-tonne Transocean Winner ran aground at Dalmore on Lewis during a towing operation and was successfully refloated after three weeks.
Now, divers are recovering about 40 pieces of debris at the bay and officials warn more could surface.
The smallest items are the size of a laptop while larger sections resemble scaffolding poles. One piece is thought to weigh about 200lbs.
All pieces which have been recovered are being landed and stored temporarily at nearby Carloway.
Colin Mulvana, the deputy secretary of state’s representative for maritime salvage and intervention, said: “The divers are working very hard to make sure that they are picking up all the bits found on site but there may well be previously undetected debris that may appear following bad weather.
“Our advice remains the same as it has from the start - please stay off the beach while the diving operation continues and while the temporary exclusion zone (TEZ) is still in place.
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‘We know that surfers and walkers, including those with dogs, use Dalmore Bay and will continue to use it after the diving operation is over and the TEZ has been lifted.
“We’d just like them to be aware of the possibility of debris washing up over the next few months. Just keep an eye out, particularly after stormy weather for anything unusual. If you do, don’t try to pick it up, just call 999 and ask for the Coastguard.”
The rig ran aground on August 8 after losing its tow en-route from Norway to Malta and was refloated three weeks later.
The semi-submersible was then towed to Broad Bay on the eastern side of Lewis, where it remains secured with eight anchors.
The rig’s grounding sparked pollution fears due to the 280 tonnes of diesel on board.
Investigations found two of its four fuel tanks were damaged in the incident which resulted in the loss of 53,000 litres of fuel, most of which is thought to have evaporated with no damage to the environment. The remaining fuel has been safely removed.
A Maritime and Coastguard Agency spokeswoman said: “There’s no sign of pollution and monitoring continues. Further assessments, including underwater surveys by remotely operated vehicles and divers, continue to take place.
“Good progress is being made but no decision has been finalised as to where the rig might be taken next.”
The Marine Accident Investigation Branch is investigating the rig’s grounding and loss of tow.