Yes the grammar checking is correct in this case. It could be correct to flank however with commas in some cases, but not in the particular case you have in your example, because it is a compound sentence.
When you are using a conjunctive adverb to combine two sentences, you should proceed the conjunctive adverb with a semicolon, as explained on grammarerrors.com:
Sometimes writers use words such as however, furthermore, and therefore (these are called conjunctive adverbs) in place of coordinating conjunctions to combine two sentences into one. This is where a punctuation problem often arises. The mistake writers make is to incorrectly place a comma in place of a semicolon before conjunctive adverbs, as illustrated in the sentence below:
Example 2: The festival was to be held today, however, it was canceled due to the rainy weather. (comma preceding the conjunctive adverb – INCORRECT. Note: The comma following the conjunctive adverb is perfectly correct and should be left as is.)
This only applies to compound sentences though.
As further explained at the above linked site:
The sporting events, however, continued despite the weather.
Is perfectly fine, as it is not a compound sentence.