The boos were sparked by a meeting in May between the midfielder met with Turkish leader Recep Tayyip and referred to him as "my president".
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It was their first win in six matches but the Germans, who leave for Russian Federation in four days, rarely put their foot on the gas, seemingly fearful of any last-minute injuries, while the Saudis confirmed their good form heading into the World Cup.
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World champions Germany failed to hit top gear as they edged to a 2-1 victory over Saudi Arabia in a lacklustre World Cup dress rehearsal on Friday, less than a week before the tournament starts.
"But [the scandal] could as well be a small aspect [in the decision-making process]".
Both players, who were born in Germany to families of Turkish descent, presented Erdogan with jerseys from their clubs, with Gundogan dedicating his Manchester City jersey to "my revered president".
Grindel later tweeted a photo of himself, Loew and team manager Oliver Bierhoff sitting down for talks with Gundogan and Ozil, saying the players "have informed us that they stand for and identify with our values on and off the pitch".
"It's obvious that the discussion over integration should not end here, and also not that over the photo", Bierhoff added. We have a lot of players in our academies with a migrant background.
Beatrix von Storch, a lawmaker for Germany's far-right AfD party, posed a question on social media asking why Gundogan was playing for Germany if Erdogan was his president. And in the wake of the Saudi game, he posted a tweet saying "Last game before the World Cup ... and still grateful to play for this country".
Bierhoff's sentiment was echoed by Germany keeper Manuel Neuer.
The Bayern Munich number one told Gazzetta dello Sport that the situation is "bothering the whole nation" and not just the two players.
Stephan Uersfeld is the Germany correspondent for ESPN FC.