As far as I know the pillowcase was retrieved by Gerry McCann on 21st May during his first return home from Portugal, although neither of the McCanns have ever confirmed this to my knowledge.
The FSS got a DNA profile from stains on the pillowcase which, they said, was from a child of the McCanns.
On 12 October 2007, the Forensic Science Service(R) received a blood spot in a cardboard frame (object JRB/1) from Leicestershire Constabulary. That object was inside a sealed package.
JRB/1 Madeleine McCann
From this sample was obtained a DNA reference sample that was different from those of her immediate family, described above. This DNA profile was the same as that obtained from possible spots of saliva existing on the pillowcase (SJM/1).
http://www.mccannpjfiles.co.uk/PJ/JOHN_LOWE.htmSo we have two matching samples. One from a pillowcase taken from Rothley and one from a blood spot in a cardboard frame provided by Leicestershire police.
In order to get Madeleine's heel prick Leicestershire Police would need a court order. Did the holders of the sample then give them just one of the spots collected? This is what the full sample is like;

I can't find anything to say the blood spot from LP was Madeleine's.
I have found a reference to the pillowcase being taken from Madeleine's home, but not who collected it.
From Jose de Freitas
New Scotland Yard to Inspector Ferreira
Inspector Ferreira,
DNA profile of Madeleine McCann that was collected in her parents house in England.
Regards
Jose de Freitas
New Scotland Yard
http://www.mccannpjfiles.co.uk/PJ/MADELEINES_DNA.htmAll we know from this is that a blood spot from [?] matched dribbles on a pillowcase from the house in Rothley, and that the dribbler was a child of the McCanns, but not one of the twins.