Recent experience with modified annual pass.
We just finished a vacation that includes visits to 6 national parks in Colorado and Utah. We got the annual pass when visiting Capitol Reef NP to save money on the remaining two visits to Bryce and Zion.
When we purchased the pass, the ranger at the kiosk told us that most parks would honor the card in the name of "customer service" as long as we only covered the likeness of the Tangerine Palpatine (our words, not his) and didn't cover anything else on either side.
When we got to Bryce Canyon, the ranger there warned us that other parks may not accept the card because it was "damaged" and she recommended we remove the sticker. I thanked her and drove away.
When we got to Zion, the ranger there told us we needed to remove the sticker and attempted to remove it. Ok asked for it back immediately fearing she would confiscate it and my wife removed the sticker.
Short version: we were able to use a modified annual pass for two parks but with a rebuke to remove our adhesive modification covering Jabba the Gut.