diff --git a/src/gpu/gl/GrGLGpu.cpp b/src/gpu/gl/GrGLGpu.cpp
index fe80ff7..e4d9cb2 100644
--- a/src/gpu/gl/GrGLGpu.cpp
+++ b/src/gpu/gl/GrGLGpu.cpp
@@ -674,6 +674,10 @@
 
     auto texture = GrGLTexture::MakeWrapped(this, mipmapStatus, desc,
                                             backendTex.getGLTextureParams(), cacheable, ioType);
+    if (this->glCaps().isFormatRenderable(backendTex.getBackendFormat(), 1)) {
+        // Pessimistically assume this external texture may have been bound to a FBO.
+        texture->baseLevelWasBoundToFBO();
+    }
     return std::move(texture);
 }