diff --git a/pygmt/helpers/utils.py b/pygmt/helpers/utils.py
index 5da09dc6e24..57319679395 100644
--- a/pygmt/helpers/utils.py
+++ b/pygmt/helpers/utils.py
@@ -150,8 +150,11 @@ def _is_ascii_no_apostrophe_and_backtick(argstr: str) -> bool:
     Check if a string only contains ASCII characters excluding apostrophe (') and
     backtick (`).
 
-    Apostrophe (') and backtick (`) are excluded because they are typographically
-    different in Adobe ISOLatin1+ encoding and need special handling.
+    For typographical reasons, apostrophe (') and backtick (`) are mapped to left and
+    right single quotation marks (‘ and ’) in Adobe ISOLatin1+ encoding. To ensure what
+    you type is what you get (https://github.com/GenericMappingTools/pygmt/issues/3476),
+    they need special handling in the non_ascii_to_octal function. Thus, the two
+    characters are excluded here.
 
     Parameters
     ----------
@@ -174,7 +177,7 @@ def _is_ascii_no_apostrophe_and_backtick(argstr: str) -> bool:
     False
     >>> _is_ascii_no_apostrophe_and_backtick("12AB±β①②")
     False
-    """
+    """  # noqa: RUF002
     return all(32 <= ord(c) <= 126 and c not in "'`" for c in argstr)
 
 
@@ -211,8 +214,7 @@ def _check_encoding(argstr: str) -> Encoding:
     'ISOLatin1+'
     """
     # Return "ascii" if the string only contains ASCII characters.
-    # Apostrophe (') and backtick (`) are excluded because they are typographically
-    # different in Adobe ISOLatin1+ encoding and need special handling.
+    # Apostrophe (') and backtick (`) are excluded.
     if _is_ascii_no_apostrophe_and_backtick(argstr):
         return "ascii"
     # Loop through all supported encodings and check if all characters in the string
@@ -412,6 +414,7 @@ def non_ascii_to_octal(argstr: str, encoding: Encoding = "ISOLatin1+") -> str:
     '12AB\\340\\341\\342\\343\\344\\345@~\\142@~@%34%\\254@%%@%34%\\255@%%'
     """  # noqa: RUF002
     # Return the input string if it only contains ASCII characters.
+    # Apostrophe (') and backtick (`) are excluded.
     if encoding == "ascii" or _is_ascii_no_apostrophe_and_backtick(argstr):
         return argstr
 
@@ -428,6 +431,11 @@ def non_ascii_to_octal(argstr: str, encoding: Encoding = "ISOLatin1+") -> str:
 
     # Remove any printable characters.
     mapping = {k: v for k, v in mapping.items() if k not in string.printable}
+
+    if encoding == "ISOLatin1+":
+        # Special handling for apostrophe (') and backtick (`).
+        # See _is_ascii_no_apostrophe_and_backtick for details.
+        mapping.update({"'": "\\234", "`": "\\140"})
     return argstr.translate(str.maketrans(mapping))