Looking closer at the question:
When did BL's parents find out that GP was dead?
There are a number of events that happened which
should have led BL's parents to question what was going on, and IMO, their actions show that they knew more about the circumstances than anyone else.
AUG 31
ACTION: RL cancels camping reservations for two people for Sep 1-3
(Did they know BL was on his way back from WY?)
SEP 1 (10:26AM) - BL arrives in North Port with the van, without GP
They knew GP was no longer with BL and the van.
SEP 4
ACTION: RL buys BL a new phone
They knew BL's prior phone was gone/missing/discarded.
SEP 6-8
ACTION: Family camping trip
(Were they trying to avoid being in an area with cell service so they would have an excuse for not answering the Petitos' calls?)
SEP 10 - They receive calls/texts from GP's family
ACTION: They do not respond to the calls
They knew GP's family was looking for her.
(Did they know by then that there was not an "innocent" explanation for GP's disappearance and that things they said could get BL into trouble?)
SEP 11 -
LE, looking for GP, seize the van from their home
ACTION: They (at some point prior to this) have hired a lawyer and have his info at the ready.
They knew that LE was looking for GP and wanted to question BL.
(Did they know by then that there was not an "innocent" explanation for GP's disappearance and that things they said could get BL into trouble?)
SEP 13 - BL leaves home (according to his parents); attorney also claims (on 9/28) that this is the last time he spoke with him (source)
ACTION: They do not report him missing immediately, despite reportedly searching for him for "hours" at the Reserve
They knew that BL was "missing"
SEP 14 - Mustang ticketed at Reserve
STATEMENT: “This is understandably an extremely difficult time for both the Petito family and the Laundrie family. It is our understanding that a search has been organized for Miss Petito in or near Grand Teton National Park in Wyoming. On behalf of the Laundrie family it is our hope that the search for Miss Petito is successful and that Miss Petito is reunited with her family. On the advice of counsel, the Laundrie family is remaining in the background at this juncture and will have no further comment.”
Source
SEP 15 - BL named person of interest
STATEMENT: “In my experience, intimate partners are often the first person law enforcement focuses their attention on in cases like this and the warning that 'any statement made will be used against you' is true, regardless of whether my client had anything to do with Ms. Petito's disappearance. As such, on the advice of counsel, Mr. Laundrie is not speaking on this matter. This formality has not really changed the circumstances of Mr. Laundrie being the focus and attention of law enforcement and Mr. Laundrie will continue to remain silent on the advice of counsel,"
Source
(
Noting here that, according to his own claims, BL's attorney had not actually spoken to BL since BL in two days, despite BL being officially declared a person of interest)
SEP 16
ACTION: Remove Mustang from the Reserve
SEP 17
ACTION: BL reported missing (by attorney)
(Why now? Could it be because this was the first day that "Spread Creek" was mentioned in the news (source)? Could his parents have known what LE would find there and needed to declare BL missing before that news broke and he was officially declared a suspect, so that they couldn't be charged with aiding a fugitive from justice?)
SEP 18 - Bethunes post the video of the van filmed at Spread Creek
SEP 19 - GP's body found
STATEMENT: “The news about Gabby Petito is heartbreaking. The Laundrie family prays for Gabby and her family.”
Source
This is the point at which everyone knew GP was dead.
(But how long had they known before this?)