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Seriously, 31 bytes (non-competing)

úúû+╗úRúûR+╝,`;╜íuWD╛E(X0WX`Mεj

Hex Dump:

a3a3962bbba352a396522bbc2c603bbda1755744be452858305758604dee6a

Try It Online

Expl:

úúû+╗ Put UPPERCASElowercase in reg0
 úRúûR+╝ Put ESACREPPUesacrewol in reg1
 , Fetch input.
 ` `Mεj Map over the characters in string as list, joining result
 ;╜íu Find 1-index of character in UPPERCASElowercase
 W 0WX If it is positive (present): 
 D Convert back to 0-index
 ╛E Look it up in ESACREPPUesacrewol
 (X Delete the original character.
 (Else just leave the original character unchanged.)

I just realized the spec say no additional whitespace, but there is no way to suppress trailing newlines in Seriously output, so there is no Seriously solution.

Seriously, 31 bytes

úúû+╗úRúûR+╝,`;╜íuWD╛E(X0WX`Mεj

Hex Dump:

a3a3962bbba352a396522bbc2c603bbda1755744be452858305758604dee6a

Try It Online

Expl:

úúû+╗ Put UPPERCASElowercase in reg0
 úRúûR+╝ Put ESACREPPUesacrewol in reg1
 , Fetch input.
 ` `Mεj Map over the characters in string as list, joining result
 ;╜íu Find 1-index of character in UPPERCASElowercase
 W 0WX If it is positive (present): 
 D Convert back to 0-index
 ╛E Look it up in ESACREPPUesacrewol
 (X Delete the original character.
 (Else just leave the original character unchanged.)

I just realized the spec say no additional whitespace, but there is no way to suppress trailing newlines in Seriously output, so there is no Seriously solution.

Seriously, 31 bytes

úúû+╗úRúûR+╝,`;╜íuWD╛E(X0WX`Mεj

Hex Dump:

a3a3962bbba352a396522bbc2c603bbda1755744be452858305758604dee6a

Try It Online

Expl:

úúû+╗ Put UPPERCASElowercase in reg0
 úRúûR+╝ Put ESACREPPUesacrewol in reg1
 , Fetch input.
 ` `Mεj Map over the characters in string as list, joining result
 ;╜íu Find 1-index of character in UPPERCASElowercase
 W 0WX If it is positive (present): 
 D Convert back to 0-index
 ╛E Look it up in ESACREPPUesacrewol
 (X Delete the original character.
 (Else just leave the original character unchanged.)

Seriously, 31 bytes (non-competing)

úúû+╗úRúûR+╝,`;╜íuWD╛E(X0WX`Mεj

Hex Dump:

a3a3962bbba352a396522bbc2c603bbda1755744be452858305758604dee6a

Try It Online

Expl:

úúû+╗ Put UPPERCASElowercase in reg0
 úRúûR+╝ Put ESACREPPUesacrewol in reg1
 , Fetch input.
 ` `Mεj Map over the characters in string as list, joining result
 ;╜íu Find 1-index of character in UPPERCASElowercase
 W 0WX If it is positive (present): 
 D Convert back to 0-index
 ╛E Look it up in ESACREPPUesacrewol
 (X Delete the original character.
 (Else just leave the original character unchanged.)

I just realized the spec say no additional whitespace, but there is no way to suppress trailing newlines in Seriously output, so there is no Seriously solution.