In 2016, Olympic National Park had 3,390,221 total visitors. I could not find data on individual national park visitation rates by international visitors.

But, statisticians at VISA have noted that visitors Asian visitors (the majority from China) that visit all of our National Parks are the fastest growing segment of visitors to the parks. Their visits grew 13 percent in 2016, higher than the 10% growth in all visitors. One in six foreign visitors to the national parks in 2016 came from the Asia Paciﬁc region. VISA also noted that Chinese visitors impact the local economy more signiﬁcantly than other foreign travelers or Americans. They spend about $85 overall while visiting the U.S for every one dollar spent on average at the national parks, compared to $50 for other foreign visitors, according to Visa estimates.
 
I don't think that we want to discourage international visits to US National Parks. Raising fees on international visitors would negatively impact local businesses.