Yes the grammar checking is correct in this case. It could be correct 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 semi-colon, as explained on [grammarerrors.com][1]:

> 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. 


  [1]: http://www.grammarerrors.com/punctuation/commas-with-conjunctive-adverbs-however-furthermore-etc/