I am sure one of our resident experts can cofirm, but in the example that you provoded, i believe the lendor would see the higher score, meaning not the one that takes that hard pull into consideration.
In the example that you gave (700 to 680), are you sure nothing else changed and that you are viewing the same CB and scoring model? Although each profile is different, 20 points sounds like a lot for an inquiry.
Year 2012: All Scores in the 520 range, during a foreclosure, CC Settlement and high UTIL. Very ugly days...
April 2023: EX8: 840; EQ8: 832; TU8: 842 -- Middle Mortgage Score: 822
In My Wallet: Discover $73.7K; Cap1 Venture $48.7K; Amex ED $38K; Amex Optima $2.5K; Amex Delta Gold $18K; Citi Costco $22.5K; Cap1 Plat $8.4K; Barclay $7K; Chase Amazon $6K; BoA Plat $21.6K; Citi TY Pref $21K; US Bank $4K; Dell $5K; Care Credit $6.5K. Total Revolving CL: $296K
My UTIL: Less than 1% - Only allow about $10 a month to report, on one account. .