Hogwarts might’ve sent them an owl asking for a gift for Harry.
The first time Hedwig comes back from the Dursleys with a “Christmas present” for Harry, she has a note from them saying they’d received a message and are sending him his present.
“A second, very small parcel contained a note.
We received your message and enclose your Christmas present. From Uncle Vernon and Aunt Petunia.
Sellotaped to the note was a fifty-pence piece.”
- Harry Potter and the Philosopher's Stone, Chapter 12 (The Mirror of Erised)
It’s unclear exactly what the message is, but it may be a message telling them to send Hedwig back with a present for Harry. If that is indeed what it was, then they may have just given Hedwig something to make her go away and leave them alone. They wouldn’t want an owl pestering them.
Hedwig herself was also determined to try to collect gifts for him.
Hedwig also did attempt to get presents from people for Harry herself. She visited Hermione in France on Harry’s birthday, and Hermione figured she wanted to ensure Harry would get a present.
“I’m on holiday in France at the moment and I didn’t know how I was going to send this to you – what if they’d opened it at Customs? – but then Hedwig turned up! I think she wanted to make sure you got something for your birthday for a change.”
- Harry Potter and the Prisoner of Azkaban, Chapter 1 (Owl Post)
Presumably from the way Hermione phrases it, Hedwig hadn’t brought a letter, she just showed up in France without a letter from Harry to see if Hermione would send a present back with her.