Probably an issue introduced in bug 1522893.
(As a side note, I'm not sure why Backspace removes the selected row but Suppr doesn't. A macOS keyboard bias maybe?)

Steps to reproduce:

1. Visit https://www.wikipedia.org/
2. Open the Storage Inspector and select Cookies > https://www.wikipedia.org
3. Double-click a value to edit it.
4. Hit the Backspace key.

Expected result: the text input's value should be cleared (if selected) or the character to the left of the caret should be removed.

Actual result: the currently selected row is removed.

Getting decent results with:

diff --git a/devtools/client/storage/ui.js b/devtools/client/storage/ui.js
--- a/devtools/client/storage/ui.js
+++ b/devtools/client/storage/ui.js
@@ -1137,10 +1137,13 @@ class StorageUI {
       this.sidebarToggledOpen = false;
       event.stopPropagation();
       event.preventDefault();
-    } else if (event.keyCode == KeyCodes.DOM_VK_BACK_SPACE && this.table.selectedRow) {
-      this.onRemoveItem();
-      event.stopPropagation();
-      event.preventDefault();
+    } else if (event.keyCode == KeyCodes.DOM_VK_BACK_SPACE ||
+      event.keyCode == KeyCodes.DOM_VK_DELETE) {
+      if (this.table.selectedRow && event.target.nodeName !== "textbox") {
+        this.onRemoveItem();
+        event.stopPropagation();
+        event.preventDefault();
+      }
     }
   }

Hey Florens, if you submit the patch I'll review and land it straight away.

I'm on something else right now but will try to push the patch soon.

David, can I pick your brain since you proposed deleting on Backspace originally? What do you think about also using the Delete key for the same action? On some keyboards (especially for Windows/Linux) I tend to use Delete more, and Backspace on macOS only for lack of a Delete key (I think you get Delete with Fn+Backspace?). Should we match both?

Yep, works for me!

https://hg.mozilla.org/mozilla-central/rev/a7af13fee7b2

Confirmed with 68.0a1(20190415213626).
Fix verified with 68.0.1, 69.0b11 on Windows 10, macOS 10.13, Ubuntu 16.04.